# output from GSASIIspc computed on platform darwin on 2013-06-02
import numpy as np
array = np.array
float32=np.float32
# testing 255 space groups (25 dups/non-standard)
SGdat = {
"p 4/n b m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 4/n b m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0.5,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0.5,  0. ], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)]]} ,
"p -4 c 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P -4 c 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)]]} ,
"r -3 m": {'SGCen': array([[ 0.        ,  0.        ,  0.        ],
       [ 0.33333333,  0.66666667,  0.66666667],
       [ 0.66666667,  0.33333333,  0.33333333]]), 'SGPolax': '', 'SGLatt': 'R', 'SpGrp': 'R -3 m', 'SGLaue': '3m1', 'SGSys': 'trigonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  1.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 1., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 42 n m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 42 n m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"a b a 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'A', 'SpGrp': 'A b a 2', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 42/m b c": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 42/m b c', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)]]} ,
"p m n 21": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P m n 21', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)]]} ,
"i 4/m c m ": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I 4/m c m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)]]} ,
"p 42/m c m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 42/m c m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p m -3": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P m -3', 'SGLaue': 'm3', 'SGSys': 'cubic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0.,  1.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0.,  1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0., -1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 1.,  0.,  0.],
       [ 0., -1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 0.,  0., -1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0., -1.],
       [-1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0., -1.],
       [-1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p b a 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P b a 2', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"i b a m": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I b a m', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 21/m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 21/m', 'SGLaue': '2/m', 'SGSys': 'monoclinic', 'SGInv': True, 'SGUniq': 'b', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0.5,  0. ], dtype=float32)]]} ,
"p 41": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 41', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.  ,  0.25], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.  ,  0.75], dtype=float32)]]} ,
"p 42": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 42', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)]]} ,
"p 43": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 43', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.  ,  0.75], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.  ,  0.25], dtype=float32)]]} ,
"f 4 3 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': '', 'SGLatt': 'F', 'SpGrp': 'F 4 3 2', 'SGLaue': 'm3m', 'SGSys': 'cubic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0.,  1.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0.,  1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0.,  1.],
       [ 0., -1.,  0.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.],
       [ 0., -1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 1.,  0.,  0.],
       [ 0., -1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 1.,  0.,  0.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 1.,  0.,  0.],
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       [ 0.,  1.,  0.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
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       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
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       [ 1.,  0.,  0.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 1.,  0.,  0.],
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       [ 0.,  1.,  0.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
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       [ 0., -1.,  0.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
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       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)]]} ,
"i b c a": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I b c a', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)]]} ,
"p 42 21 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 42 21 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"f m m m": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': '', 'SGLatt': 'F', 'SpGrp': 'F m m m', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"i 41": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'I', 'SpGrp': 'I 41', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.5 ,  0.25], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5 ,  0.  ,  0.75], dtype=float32)]]} ,
"p 6": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 6', 'SGLaue': '6/m', 'SGSys': 'hexagonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  1.,  0.],
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       [-1.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 3": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 3', 'SGLaue': '3', 'SGSys': 'trigonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p m m n": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P m m n', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0.5,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)]]} ,
"p m m m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P m m m', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"r 3 m h": {'SGCen': array([[ 0.        ,  0.        ,  0.        ],
       [ 0.33333333,  0.66666667,  0.66666667],
       [ 0.66666667,  0.33333333,  0.33333333]]), 'SGPolax': 'z', 'SGLatt': 'R', 'SpGrp': 'R 3 m h', 'SGLaue': '3m1', 'SGSys': 'trigonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 1., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"c m c 21": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': 'z', 'SGLatt': 'C', 'SpGrp': 'C m c 21', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)]]} ,
"p 1": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'xyz', 'SGLatt': 'P', 'SpGrp': 'P 1', 'SGLaue': '-1', 'SGSys': 'triclinic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"i 4": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'I', 'SpGrp': 'I 4', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 4": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 4', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 42 b c": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 42 b c', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0., -1.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)]]} ,
"p m m a": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P m m a', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0. ], dtype=float32)]]} ,
"i -4 m 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I -4 m 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
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       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p -4 21 c": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P -4 21 c', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
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       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0.5], dtype=float32)]]} ,
"p 4 2 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 4 2 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.5,  0.5,  0. ]]), 'SGPolax': 'y', 'SGLatt': 'C', 'SpGrp': 'C 1 2 1', 'SGLaue': '2/m', 'SGSys': 'monoclinic', 'SGInv': False, 'SGUniq': 'b', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p b c n": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P b c n', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"a m m 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'A', 'SpGrp': 'A m m 2', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"i m -3 m": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I m -3 m', 'SGLaue': 'm3m', 'SGSys': 'cubic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 0.5,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'I', 'SpGrp': 'I 4 m m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"i m m 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'I', 'SpGrp': 'I m m 2', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 42/n c m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 42/n c m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 63": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 63', 'SGLaue': '6/m', 'SGSys': 'hexagonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 42/m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 42/m', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p m c 21": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P m c 21', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 42/n": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 42/n', 'SGLaue': '4/m', 'SGSys': 'tetragonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"a m a 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'A', 'SpGrp': 'A m a 2', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 6/m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 6/m', 'SGLaue': '6/m', 'SGSys': 'hexagonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p -6 c 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P -6 c 2', 'SGLaue': '6/mmm', 'SGSys': 'hexagonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"i -4 c 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I -4 c 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"F -1": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': '', 'SGLatt': 'F', 'SpGrp': 'F -1', 'SGLaue': '-1', 'SGSys': 'triclinic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"c c c a": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': '', 'SGLatt': 'C', 'SpGrp': 'C c c a', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"i 41 m d": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'I', 'SpGrp': 'I 41 m d', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"c c c m": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': '', 'SGLatt': 'C', 'SpGrp': 'C c c m', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 41 21 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 41 21 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 31": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 31', 'SGLaue': '3', 'SGSys': 'trigonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"p 32": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 32', 'SGLaue': '3', 'SGSys': 'trigonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"i 41 2 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0.5,  0.5]]), 'SGPolax': '', 'SGLatt': 'I', 'SpGrp': 'I 41 2 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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"a b m 2": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5]]), 'SGPolax': 'z', 'SGLatt': 'A', 'SpGrp': 'A b m 2', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
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       [ 1.,  0.,  0.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 1.,  0.,  0.],
       [ 0., -1.,  0.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 0.,  0., -1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0., -1.],
       [-1.,  0.,  0.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
       [-1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0.,  1.],
       [ 0.,  1.,  0.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 0.,  1.,  0.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0.,  0., -1.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 0.,  1.,  0.],
       [-1.,  0.,  0.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  0., -1.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0.,  0., -1.],
       [ 0., -1.,  0.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 0., -1.,  0.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)]]} ,
"p 42 c m": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 42 c m', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 6/m 1 1": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 6/m 1 1', 'SGLaue': '6/m', 'SGSys': 'hexagonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)]]} ,
"p 21 21 21": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 21 21 21', 'SGLaue': 'mmm', 'SGSys': 'orthorhombic', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0.5,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0. ,  0.5], dtype=float32)]]} ,
"f d -3": {'SGCen': array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ]]), 'SGPolax': '', 'SGLatt': 'F', 'SpGrp': 'F d -3', 'SGLaue': 'm3', 'SGSys': 'cubic', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  0.,  1.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0.,  1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.25,  0.25,  0.  ], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.  ,  0.25,  0.25], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0., -1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.25,  0.  ,  0.25], dtype=float32)], [array([[ 0.,  0., -1.],
       [ 1.,  0.,  0.],
       [ 0., -1.,  0.]], dtype=float32), array([ 0.25,  0.5 ,  0.75], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 0.,  0., -1.],
       [ 1.,  0.,  0.]], dtype=float32), array([ 0.75,  0.25,  0.5 ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 0.,  0., -1.],
       [-1.,  0.,  0.]], dtype=float32), array([ 0.5 ,  0.25,  0.75], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.75,  0.5 ,  0.25], dtype=float32)], [array([[ 0.,  0., -1.],
       [-1.,  0.,  0.],
       [ 0.,  1.,  0.]], dtype=float32), array([ 0.25,  0.75,  0.5 ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5 ,  0.75,  0.25], dtype=float32)]]} ,
"p -4 b 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P -4 b 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.5,  0.5,  0. ], dtype=float32)]]} ,
"p 3 1 c": {'SGCen': array([[0, 0, 0]]), 'SGPolax': 'z', 'SGLatt': 'P', 'SpGrp': 'P 3 1 c', 'SGLaue': '31m', 'SGSys': 'trigonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[-1.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[-1.,  0.,  0.],
       [-1.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 1., -1.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)]]} ,
"p 41 2 2": {'SGCen': array([[0, 0, 0]]), 'SGPolax': '', 'SGLatt': 'P', 'SpGrp': 'P 41 2 2', 'SGLaue': '4/mmm', 'SGSys': 'tetragonal', 'SGInv': False, 'SGUniq': '', 'SGOps': [[array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.  ,  0.25], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0.,  1.]], dtype=float32), array([ 0.  ,  0.  ,  0.75], dtype=float32)], [array([[-1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.,  0.,  0.], dtype=float32)], [array([[ 0., -1.,  0.],
       [-1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.  ,  0.  ,  0.25], dtype=float32)], [array([[ 1.,  0.,  0.],
       [ 0., -1.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0. ,  0. ,  0.5], dtype=float32)], [array([[ 0.,  1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0., -1.]], dtype=float32), array([ 0.  ,  0.  ,  0.75], dtype=float32)]]} ,
}
SGlist = {
"p 4/n b m": [' Space Group: P 4/n b m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,    Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,    Z \t', ' ( 5)    -X ,1/2+Y ,    Z \t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7) 1/2+X ,   -Y ,    Z \t( 8) 1/2+Y ,1/2+X ,    Z \t', ' '] ,
"p -4 c 2": [' Space Group: P -4 c 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)     Y ,    X ,1/2-Z \t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)    -Y ,   -X ,1/2-Z \t', ' '] ,
"r -3 m": [' Space Group: R -3 m', ' The lattice is centrosymmetric R-centered trigonal', ' Multiplicity of a general site is 36', ' The Laue symmetry is 3m1', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,    Z \t\t', ' ( 5)    -Y ,   -X ,    Z \t\t( 6)     X ,   X-Y,    Z \t\t', ' '] ,
"p 42 n m": [' Space Group: P 42 n m', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,1/2+X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4) 1/2+Y ,1/2-X ,1/2+Z \t', ' ( 5) 1/2-X ,1/2+Y ,1/2+Z \t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7) 1/2+X ,1/2-Y ,1/2+Z \t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"a b a 2": [' Space Group: A b a 2', ' The lattice is noncentrosymmetric A-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3) 1/2+X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 42/m b c": [' Space Group: P 42/m b c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5) 1/2-X ,1/2+Y ,    Z \t( 6) 1/2-Y ,1/2-X ,1/2+Z \t', ' ( 7) 1/2+X ,1/2-Y ,    Z \t( 8) 1/2+Y ,1/2+X ,1/2+Z \t', ' '] ,
"p m n 21": [' Space Group: P m n 21', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3) 1/2+X ,   -Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"i 4/m c m ": [' Space Group: I 4/m c m', ' The lattice is centrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 32', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"p 42/m c m": [' Space Group: P 42/m c m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"p m -3": [' Space Group: P m -3', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' '] ,
"p b a 2": [' Space Group: P b a 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3) 1/2+X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"i b a m": [' Space Group: I b a m', ' The lattice is centrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3) 1/2+X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 21/m": [' Space Group: P 21/m', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,   -Z \t', ' '] ,
"p 41": [' Space Group: P 41', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 4', ' The Laue symmetry is 4/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/4+Z \t', ' ( 3)    -X ,   -Y ,1/2+Z \t( 4)     Y ,   -X ,3/4+Z \t', ' '] ,
"p 42": [' Space Group: P 42', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 4', ' The Laue symmetry is 4/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' '] ,
"p 43": [' Space Group: P 43', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 4', ' The Laue symmetry is 4/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,3/4+Z \t', ' ( 3)    -X ,   -Y ,1/2+Z \t( 4)     Y ,   -X ,1/4+Z \t', ' '] ,
"f 4 3 2": [' Space Group: F 4 3 2', ' The lattice is noncentrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)    -Y ,    X ,    Z \t\t', ' ( 5)     Z ,   -Y ,    X \t\t( 6)     X ,    Z ,   -Y \t\t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13)     Y ,   -X ,    Z \t\t(14)     Z ,    Y ,   -X \t\t', ' (15)    -X ,    Z ,    Y \t\t(16)    -X ,   -Z ,   -Y \t\t', ' (17)    -Y ,   -X ,   -Z \t\t(18)    -Z ,   -Y ,   -X \t\t', ' (19)     Y ,   -Z ,   -X \t\t(20)     Y ,    X ,   -Z \t\t', ' (21)    -Z ,    Y ,    X \t\t(22)     X ,   -Z ,    Y \t\t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"p -4 21 m": [' Space Group: P -4 21 m', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,   -Z \t( 6) 1/2+Y ,1/2+X ,    Z \t', ' ( 7) 1/2+X ,1/2-Y ,   -Z \t( 8) 1/2-Y ,1/2-X ,    Z \t', ' '] ,
"p 63/m c m": [' Space Group: P 63/m c m', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 24', ' The Laue symmetry is 6/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' ( 7)    Y-X,    Y ,1/2+Z \t( 8)    -X ,   Y-X,    Z \t\t', ' ( 9)    -Y ,   -X ,1/2+Z \t(10)    X-Y,   -Y ,    Z \t\t', ' (11)     X ,   X-Y,1/2+Z \t(12)     Y ,    X ,    Z \t\t', ' '] ,
"p 2 3": [' Space Group: P 2 3', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 12', ' The Laue symmetry is m3', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,   -Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,   -Y \t\t( 6)    -Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,   -X ,    Y \t\t( 8)     Y ,   -Z ,   -X \t\t', ' ( 9)    -Y ,    Z ,   -X \t\t(10)    -X ,   -Y ,    Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -X ,    Y ,   -Z \t\t', ' '] ,
"i a 3": [' Space Group: I a 3', ' The lattice is centrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,    Y ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+X ,    Y \t( 6)     Y ,1/2-Z ,1/2+X \t', ' ( 7)    -Z ,1/2+X ,1/2-Y \t( 8) 1/2-Y ,   -Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/2-Z ,   -X \t(10)    -X ,1/2+Y ,1/2-Z \t', ' (11) 1/2-Z ,   -X ,1/2+Y \t(12) 1/2+X ,1/2-Y ,   -Z \t', ' '] ,
"p 3 2 1": [' Space Group: P 3 2 1', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3m1', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,   -Z \t\t', ' ( 5)    -X ,   Y-X,   -Z \t\t( 6)    X-Y,   -Y ,   -Z \t\t', ' '] ,
"i a -3 d": [' Space Group: I a -3 d', ' The lattice is centrosymmetric I-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,    Y ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+X ,    Y \t( 6)     Y ,1/2-Z ,1/2+X \t', ' ( 7)    -Z ,1/2+X ,1/2-Y \t( 8) 1/2-Y ,   -Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/2-Z ,   -X \t(10)    -X ,1/2+Y ,1/2-Z \t', ' (11) 1/2-Z ,   -X ,1/2+Y \t(12) 1/2+X ,1/2-Y ,   -Z \t', ' (13) 1/4+Y ,1/4+X ,1/4+Z \t(14) 1/4+Z ,1/4+Y ,1/4+X \t', ' (15) 1/4+X ,1/4+Z ,1/4+Y \t(16) 3/4+Y ,1/4+X ,1/4-Z \t', ' (17) 1/4-Z ,3/4+Y ,1/4+X \t(18) 1/4+X ,1/4-Z ,3/4+Y \t', ' (19) 3/4-Z ,3/4+Y ,1/4-X \t(20) 1/4-X ,3/4-Z ,3/4+Y \t', ' (21) 3/4+X ,1/4-Z ,3/4-Y \t(22) 3/4-Y ,3/4+X ,1/4-Z \t', ' (23) 1/4-Z ,3/4-Y ,3/4+X \t(24) 3/4+Y ,1/4-X ,3/4-Z \t', ' '] ,
"p a -3": [' Space Group: P a -3', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,    Y ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+X ,    Y \t( 6)     Y ,1/2-Z ,1/2+X \t', ' ( 7)    -Z ,1/2+X ,1/2-Y \t( 8) 1/2-Y ,   -Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/2-Z ,   -X \t(10)    -X ,1/2+Y ,1/2-Z \t', ' (11) 1/2-Z ,   -X ,1/2+Y \t(12) 1/2+X ,1/2-Y ,   -Z \t', ' '] ,
"c 2": [' Space Group: C 2', ' The lattice is noncentrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in y', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,   -Z \t\t', ' '] ,
"r 3 2 h": [' Space Group: R 3 2 h', ' The lattice is noncentrosymmetric R-centered trigonal', ' Multiplicity of a general site is 18', ' The Laue symmetry is 3m1', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,   -Z \t\t', ' ( 5)    -X ,   Y-X,   -Z \t\t( 6)    X-Y,   -Y ,   -Z \t\t', ' '] ,
"p c": [' Space Group: P c', ' The lattice is noncentrosymmetric primitive monoclinic', ' Multiplicity of a general site is 2', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in x z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,1/2+Z \t', ' '] ,
"f 2 2 2": [' Space Group: F 2 2 2', ' The lattice is noncentrosymmetric F-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,   -Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 6 c c": [' Space Group: P 6 c c', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' ( 7)    Y-X,    Y ,1/2+Z \t( 8)    -X ,   Y-X,1/2+Z \t', ' ( 9)    -Y ,   -X ,1/2+Z \t(10)    X-Y,   -Y ,1/2+Z \t', ' (11)     X ,   X-Y,1/2+Z \t(12)     Y ,    X ,1/2+Z \t', ' '] ,
"r 3 2 r": [' Space Group: R 3 2 r', ' The lattice is noncentrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3mR', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)    -Y ,   -X ,   -Z \t\t', ' ( 5)    -Z ,   -Y ,   -X \t\t( 6)    -X ,   -Z ,   -Y \t\t', ' '] ,
"p 62 2 2": [' Space Group: P 62 2 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/3+Z \t', ' ( 3)    -Y ,   X-Y,2/3+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,1/3+Z \t( 6)     Y ,   Y-X,2/3+Z \t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)     X ,   X-Y,1/3-Z \t', ' ( 9)     Y ,    X ,2/3-Z \t(10)    Y-X,    Y ,   -Z \t\t', ' (11)    -X ,   Y-X,1/3-Z \t(12)    -Y ,   -X ,2/3-Z \t', ' '] ,
"i 41 c d": [' Space Group: I 41 c d', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,1/2+X ,1/4+Z \t', ' ( 3) 1/2-X ,1/2-Y ,1/2+Z \t( 4) 1/2+Y ,   -X ,3/4+Z \t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,1/2-X ,3/4+Z \t', ' ( 7) 1/2+X ,1/2-Y ,    Z \t( 8) 1/2+Y ,    X ,1/4+Z \t', ' '] ,
"f m m 2": [' Space Group: F m m 2', ' The lattice is noncentrosymmetric F-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p m m 2": [' Space Group: P m m 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p m": [' Space Group: P m', ' The lattice is noncentrosymmetric primitive monoclinic', ' Multiplicity of a general site is 2', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in x z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,    Z \t\t', ' '] ,
"i 4 2 2": [' Space Group: I 4 2 2', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)    -Y ,   -X ,   -Z \t\t', ' ( 7)     X ,   -Y ,   -Z \t\t( 8)     Y ,    X ,   -Z \t\t', ' '] ,
"p 31 2 1": [' Space Group: P 31 2 1', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3m1', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,1/3+Z \t', ' ( 3)    Y-X,   -X ,2/3+Z \t( 4)     Y ,    X ,   -Z \t\t', ' ( 5)    -X ,   Y-X,1/3-Z \t( 6)    X-Y,   -Y ,2/3-Z \t', ' '] ,
"i -4": [' Space Group: I -4', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' '] ,
"p 2": [' Space Group: P 2', ' The lattice is noncentrosymmetric primitive monoclinic', ' Multiplicity of a general site is 2', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in y', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,   -Z \t\t', ' '] ,
"p 21 21 2": [' Space Group: P 21 21 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2+X ,1/2-Y ,   -Z \t', ' ( 3) 1/2-X ,1/2+Y ,   -Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"c 1 2/c 1": [' Space Group: C 1 2/c 1', ' The lattice is centrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 8', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2-Z \t', ' '] ,
"i b a 2": [' Space Group: I b a 2', ' The lattice is noncentrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3) 1/2+X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p b a m": [' Space Group: P b a m', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3) 1/2+X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p b a n": [' Space Group: P b a n', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,    Z \t', ' ( 3) 1/2+X ,   -Y ,    Z \t( 4) 1/2-X ,1/2-Y ,    Z \t', ' '] ,
"p m -3 n": [' Space Group: P m -3 n', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' (13) 1/2+Y ,1/2+X ,1/2+Z \t(14) 1/2+Z ,1/2+Y ,1/2+X \t', ' (15) 1/2+X ,1/2+Z ,1/2+Y \t(16) 1/2+Y ,1/2+X ,1/2-Z \t', ' (17) 1/2-Z ,1/2+Y ,1/2+X \t(18) 1/2+X ,1/2-Z ,1/2+Y \t', ' (19) 1/2-Z ,1/2+Y ,1/2-X \t(20) 1/2-X ,1/2-Z ,1/2+Y \t', ' (21) 1/2+X ,1/2-Z ,1/2-Y \t(22) 1/2-Y ,1/2+X ,1/2-Z \t', ' (23) 1/2-Z ,1/2-Y ,1/2+X \t(24) 1/2+Y ,1/2-X ,1/2-Z \t', ' '] ,
"i b c a": [' Space Group: I b c a', ' The lattice is centrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3)     X ,1/2-Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"p 42 21 2": [' Space Group: P 42 21 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,1/2+X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4) 1/2+Y ,1/2-X ,1/2+Z \t', ' ( 5) 1/2-X ,1/2+Y ,1/2-Z \t( 6)    -Y ,   -X ,   -Z \t\t', ' ( 7) 1/2+X ,1/2-Y ,1/2-Z \t( 8)     Y ,    X ,   -Z \t\t', ' '] ,
"f m m m": [' Space Group: F m m m', ' The lattice is centrosymmetric F-centered orthorhombic', ' Multiplicity of a general site is 32', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"i 41": [' Space Group: I 41', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,1/2+X ,1/4+Z \t', ' ( 3) 1/2-X ,1/2-Y ,1/2+Z \t( 4) 1/2+Y ,   -X ,3/4+Z \t', ' '] ,
"p 6": [' Space Group: P 6', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' '] ,
"p 3": [' Space Group: P 3', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 3', ' The Laue symmetry is 3', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t'] ,
"p m m n": [' Space Group: P m m n', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,    Z \t', ' ( 3)     X ,1/2-Y ,    Z \t( 4) 1/2-X ,1/2-Y ,    Z \t', ' '] ,
"p m m m": [' Space Group: P m m m', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"r 3 m h": [' Space Group: R 3 m h', ' The lattice is noncentrosymmetric R-centered trigonal', ' Multiplicity of a general site is 18', ' The Laue symmetry is 3m1', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,    Z \t\t', ' ( 5)    -Y ,   -X ,    Z \t\t( 6)     X ,   X-Y,    Z \t\t', ' '] ,
"c m c 21": [' Space Group: C m c 21', ' The lattice is noncentrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"p 1": [' Space Group: P 1', ' The lattice is noncentrosymmetric primitive triclinic', ' Multiplicity of a general site is 1', ' The Laue symmetry is -1', ' The location of the origin is arbitrary in xyz', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t'] ,
"i 4": [' Space Group: I 4', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' '] ,
"p 4": [' Space Group: P 4', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 4', ' The Laue symmetry is 4/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' '] ,
"p 42 b c": [' Space Group: P 42 b c', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5) 1/2-X ,1/2+Y ,    Z \t( 6) 1/2-Y ,1/2-X ,1/2+Z \t', ' ( 7) 1/2+X ,1/2-Y ,    Z \t( 8) 1/2+Y ,1/2+X ,1/2+Z \t', ' '] ,
"p m m a": [' Space Group: P m m a', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,    Z \t', ' ( 3)     X ,   -Y ,    Z \t\t( 4) 1/2-X ,   -Y ,    Z \t', ' '] ,
"i -4 m 2": [' Space Group: I -4 m 2', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)     Y ,    X ,   -Z \t\t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)    -Y ,   -X ,   -Z \t\t', ' '] ,
"p -4 21 c": [' Space Group: P -4 21 c', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,1/2-Z \t( 6) 1/2+Y ,1/2+X ,1/2+Z \t', ' ( 7) 1/2+X ,1/2-Y ,1/2-Z \t( 8) 1/2-Y ,1/2-X ,1/2+Z \t', ' '] ,
"p 4 2 2": [' Space Group: P 4 2 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)    -Y ,   -X ,   -Z \t\t', ' ( 7)     X ,   -Y ,   -Z \t\t( 8)     Y ,    X ,   -Z \t\t', ' '] ,
"p 4/m c c": [' Space Group: P 4/m c c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"p -6 2 m": [' Space Group: P -6 2 m', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    Y-X,   -X ,   -Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)    -Y ,   X-Y,   -Z \t\t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)    -X ,   Y-X,    Z \t\t', ' ( 9)     Y ,    X ,   -Z \t\t(10)    X-Y,   -Y ,    Z \t\t', ' (11)    -X ,   Y-X,   -Z \t\t(12)     Y ,    X ,    Z \t\t', ' '] ,
"p 1 2/m 1": [' Space Group: P 1 2/m 1', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,   -Z \t\t', ' '] ,
"p -6 2 c": [' Space Group: P -6 2 c', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    Y-X,   -X ,1/2-Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)     X ,    Y ,1/2-Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)    -Y ,   X-Y,1/2-Z \t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)    -X ,   Y-X,1/2+Z \t', ' ( 9)     Y ,    X ,   -Z \t\t(10)    X-Y,   -Y ,1/2+Z \t', ' (11)    -X ,   Y-X,   -Z \t\t(12)     Y ,    X ,1/2+Z \t', ' '] ,
"p 6 m m": [' Space Group: P 6 m m', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' ( 7)    Y-X,    Y ,    Z \t\t( 8)    -X ,   Y-X,    Z \t\t', ' ( 9)    -Y ,   -X ,    Z \t\t(10)    X-Y,   -Y ,    Z \t\t', ' (11)     X ,   X-Y,    Z \t\t(12)     Y ,    X ,    Z \t\t', ' '] ,
"c c": [' Space Group: C c', ' The lattice is noncentrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in x z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,1/2+Z \t', ' '] ,
"p 43 3 2": [' Space Group: P 43 3 2', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 3/4-Y ,1/4+X ,3/4+Z \t', ' ( 5) 3/4+Z ,3/4-Y ,1/4+X \t( 6) 1/4+X ,3/4+Z ,3/4-Y \t', ' ( 7) 1/2-X ,   -Y ,1/2+Z \t( 8)    -Z ,1/2+X ,1/2-Y \t', ' ( 9) 1/2-Y ,   -Z ,1/2+X \t(10) 1/2+X ,1/2-Y ,   -Z \t', ' (11) 1/2+Z ,1/2-X ,   -Y \t(12)    -Y ,1/2+Z ,1/2-X \t', ' (13) 3/4+Y ,3/4-X ,1/4+Z \t(14) 1/4+Z ,3/4+Y ,3/4-X \t', ' (15) 3/4-X ,1/4+Z ,3/4+Y \t(16) 1/4-X ,1/4-Z ,1/4-Y \t', ' (17) 1/4-Y ,1/4-X ,1/4-Z \t(18) 1/4-Z ,1/4-Y ,1/4-X \t', ' (19) 1/2+Y ,1/2-Z ,   -X \t(20) 1/4+Y ,3/4+X ,3/4-Z \t', ' (21) 3/4-Z ,1/4+Y ,3/4+X \t(22) 3/4+X ,3/4-Z ,1/4+Y \t', ' (23)    -X ,1/2+Y ,1/2-Z \t(24) 1/2-Z ,   -X ,1/2+Y \t', ' '] ,
"a 2 2 2": [' Space Group: A 2 2 2', ' The lattice is noncentrosymmetric A-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,   -Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p -3": [' Space Group: P -3', ' The lattice is centrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t'] ,
"p -1": [' Space Group: P -1', ' The lattice is centrosymmetric primitive triclinic', ' Multiplicity of a general site is 2', ' The Laue symmetry is -1', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t'] ,
"f d d 2": [' Space Group: F d d 2', ' The lattice is noncentrosymmetric F-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/4-X ,1/4+Y ,1/4+Z \t', ' ( 3) 1/4+X ,1/4-Y ,1/4+Z \t( 4)    -X ,1/2-Y ,1/2+Z \t', ' '] ,
"p 62": [' Space Group: P 62', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/3+Z \t', ' ( 3)    -Y ,   X-Y,2/3+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,1/3+Z \t( 6)     Y ,   Y-X,2/3+Z \t', ' '] ,
"c m m a": [' Space Group: C m m a', ' The lattice is centrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,1/2-Y ,    Z \t( 4)    -X ,1/2-Y ,    Z \t', ' '] ,
"p -3 c 1": [' Space Group: P -3 c 1', ' The lattice is centrosymmetric primitive trigonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 3m1', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,1/2+Z \t', ' ( 5)    -Y ,   -X ,1/2+Z \t( 6)     X ,   X-Y,1/2+Z \t', ' '] ,
"c m c m": [' Space Group: C m c m', ' The lattice is centrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"c m m m": [' Space Group: C m m m', ' The lattice is centrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"c m c a": [' Space Group: C m c a', ' The lattice is centrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,1/2-Y ,1/2+Z \t( 4)    -X ,1/2-Y ,1/2+Z \t', ' '] ,
"i a -3": [' Space Group: I a -3', ' The lattice is centrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,    Y ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+X ,    Y \t( 6)     Y ,1/2-Z ,1/2+X \t', ' ( 7)    -Z ,1/2+X ,1/2-Y \t( 8) 1/2-Y ,   -Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/2-Z ,   -X \t(10)    -X ,1/2+Y ,1/2-Z \t', ' (11) 1/2-Z ,   -X ,1/2+Y \t(12) 1/2+X ,1/2-Y ,   -Z \t', ' '] ,
"i m a 2": [' Space Group: I m a 2', ' The lattice is noncentrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,    Z \t', ' ( 3) 1/2+X ,   -Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 63/m m c": [' Space Group: P 63/m m c', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 24', ' The Laue symmetry is 6/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' ( 7)    Y-X,    Y ,    Z \t\t( 8)    -X ,   Y-X,1/2+Z \t', ' ( 9)    -Y ,   -X ,    Z \t\t(10)    X-Y,   -Y ,1/2+Z \t', ' (11)     X ,   X-Y,    Z \t\t(12)     Y ,    X ,1/2+Z \t', ' '] ,
"p 4 3 2": [' Space Group: P 4 3 2', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)    -Y ,    X ,    Z \t\t', ' ( 5)     Z ,   -Y ,    X \t\t( 6)     X ,    Z ,   -Y \t\t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13)     Y ,   -X ,    Z \t\t(14)     Z ,    Y ,   -X \t\t', ' (15)    -X ,    Z ,    Y \t\t(16)    -X ,   -Z ,   -Y \t\t', ' (17)    -Y ,   -X ,   -Z \t\t(18)    -Z ,   -Y ,   -X \t\t', ' (19)     Y ,   -Z ,   -X \t\t(20)     Y ,    X ,   -Z \t\t', ' (21)    -Z ,    Y ,    X \t\t(22)     X ,   -Z ,    Y \t\t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"i 41/a c d": [' Space Group: I 41/a c d', ' The lattice is centrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 32', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/4-Y ,3/4+X ,1/4+Z \t', ' ( 3) 1/2-X ,   -Y ,1/2+Z \t( 4) 1/4+Y ,1/4-X ,3/4+Z \t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6) 1/4-Y ,3/4-X ,3/4+Z \t', ' ( 7) 1/2+X ,   -Y ,    Z \t( 8) 1/4+Y ,1/4+X ,1/4+Z \t', ' '] ,
"p -4 2 c": [' Space Group: P -4 2 c', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,1/2-Z \t( 6)     Y ,    X ,1/2+Z \t', ' ( 7)     X ,   -Y ,1/2-Z \t( 8)    -Y ,   -X ,1/2+Z \t', ' '] ,
"p 4 n c": [' Space Group: P 4 n c', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,1/2+Z \t( 6) 1/2-Y ,1/2-X ,1/2+Z \t', ' ( 7) 1/2+X ,1/2-Y ,1/2+Z \t( 8) 1/2+Y ,1/2+X ,1/2+Z \t', ' '] ,
"p 4/m": [' Space Group: P 4/m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' '] ,
"p 4/n": [' Space Group: P 4/n', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,    Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,    Z \t', ' '] ,
"p 21/c": [' Space Group: P 21/c', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,1/2-Z \t', ' '] ,
"r -3 c": [' Space Group: R -3 c', ' The lattice is centrosymmetric R-centered trigonal', ' Multiplicity of a general site is 36', ' The Laue symmetry is 3m1', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,1/2+Z \t', ' ( 5)    -Y ,   -X ,1/2+Z \t( 6)     X ,   X-Y,1/2+Z \t', ' '] ,
"p 4/n m m": [' Space Group: P 4/n m m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,    Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,    Z \t', ' ( 5) 1/2-X ,    Y ,    Z \t( 6) 1/2-Y ,1/2-X ,    Z \t', ' ( 7)     X ,1/2-Y ,    Z \t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"i 4/m": [' Space Group: I 4/m', ' The lattice is centrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' '] ,
"p 3 m 1": [' Space Group: P 3 m 1', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3m1', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,    Z \t\t', ' ( 5)    -Y ,   -X ,    Z \t\t( 6)     X ,   X-Y,    Z \t\t', ' '] ,
"p 63/m": [' Space Group: P 63/m', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' '] ,
"p 6 2 2": [' Space Group: P 6 2 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)     X ,   X-Y,   -Z \t\t', ' ( 9)     Y ,    X ,   -Z \t\t(10)    Y-X,    Y ,   -Z \t\t', ' (11)    -X ,   Y-X,   -Z \t\t(12)    -Y ,   -X ,   -Z \t\t', ' '] ,
"p 2/m": [' Space Group: P 2/m', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,   -Z \t\t', ' '] ,
"f d 3": [' Space Group: F d 3', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/4+X ,1/4+Y ,   -Z \t', ' ( 5)    -Z ,1/4+X ,1/4+Y \t( 6) 1/4+Y ,   -Z ,1/4+X \t', ' ( 7) 1/4-Z ,1/2+X ,3/4-Y \t( 8) 3/4-Y ,1/4-Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/4-Z ,3/4-X \t(10) 3/4-X ,1/2+Y ,1/4-Z \t', ' (11) 1/4-Z ,3/4-X ,1/2+Y \t(12) 1/2+X ,3/4-Y ,1/4-Z \t', ' '] ,
"i 41/a m d": [' Space Group: I 41/a m d', ' The lattice is centrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 32', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/4-Y ,3/4+X ,1/4+Z \t', ' ( 3) 1/2-X ,   -Y ,1/2+Z \t( 4) 1/4+Y ,1/4-X ,3/4+Z \t', ' ( 5)    -X ,    Y ,    Z \t\t( 6) 1/4-Y ,3/4-X ,1/4+Z \t', ' ( 7) 1/2+X ,   -Y ,1/2+Z \t( 8) 1/4+Y ,1/4+X ,3/4+Z \t', ' '] ,
"p 4/n c c": [' Space Group: P 4/n c c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,    Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,    Z \t', ' ( 5) 1/2-X ,    Y ,1/2+Z \t( 6) 1/2-Y ,1/2-X ,1/2+Z \t', ' ( 7)     X ,1/2-Y ,1/2+Z \t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"i m m a": [' Space Group: I m m a', ' The lattice is centrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,1/2-Y ,    Z \t( 4)    -X ,1/2-Y ,    Z \t', ' '] ,
"p 4 b m": [' Space Group: P 4 b m', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,    Z \t( 6) 1/2-Y ,1/2-X ,    Z \t', ' ( 7) 1/2+X ,1/2-Y ,    Z \t( 8) 1/2+Y ,1/2+X ,    Z \t', ' '] ,
"p 2/c": [' Space Group: P 2/c', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2-Z \t', ' '] ,
"p -6 m 2": [' Space Group: P -6 m 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    Y-X,   -X ,   -Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)    -Y ,   X-Y,   -Z \t\t', ' ( 7)    Y-X,    Y ,    Z \t\t( 8)     X ,   X-Y,   -Z \t\t', ' ( 9)    -Y ,   -X ,    Z \t\t(10)    Y-X,    Y ,   -Z \t\t', ' (11)     X ,   X-Y,    Z \t\t(12)    -Y ,   -X ,   -Z \t\t', ' '] ,
"p n n 2": [' Space Group: P n n 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,1/2+Z \t', ' ( 3) 1/2+X ,1/2-Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 31 1 2": [' Space Group: P 31 1 2', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 31m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,1/3+Z \t', ' ( 3)    Y-X,   -X ,2/3+Z \t( 4)     X ,   X-Y,   -Z \t\t', ' ( 5)    Y-X,    Y ,1/3-Z \t( 6)    -Y ,   -X ,2/3-Z \t', ' '] ,
"f -4 3 c": [' Space Group: F -4 3 c', ' The lattice is noncentrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+Y ,1/2-X ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+Y ,1/2-X \t( 6) 1/2-X ,1/2-Z ,1/2+Y \t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13) 1/2-Y ,1/2+X ,1/2-Z \t(14) 1/2-Z ,1/2-Y ,1/2+X \t', ' (15) 1/2+X ,1/2-Z ,1/2-Y \t(16) 1/2+X ,1/2+Z ,1/2+Y \t', ' (17) 1/2+Y ,1/2+X ,1/2+Z \t(18) 1/2+Z ,1/2+Y ,1/2+X \t', ' (19)     Y ,   -Z ,   -X \t\t(20) 1/2-Y ,1/2-X ,1/2+Z \t', ' (21) 1/2+Z ,1/2-Y ,1/2-X \t(22) 1/2-X ,1/2+Z ,1/2-Y \t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"i m -3": [' Space Group: I m -3', ' The lattice is centrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' '] ,
"f -4 3 m": [' Space Group: F -4 3 m', ' The lattice is noncentrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     Y ,   -X ,   -Z \t\t', ' ( 5)    -Z ,    Y ,   -X \t\t( 6)    -X ,   -Z ,    Y \t\t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13)    -Y ,    X ,   -Z \t\t(14)    -Z ,   -Y ,    X \t\t', ' (15)     X ,   -Z ,   -Y \t\t(16)     X ,    Z ,    Y \t\t', ' (17)     Y ,    X ,    Z \t\t(18)     Z ,    Y ,    X \t\t', ' (19)     Y ,   -Z ,   -X \t\t(20)    -Y ,   -X ,    Z \t\t', ' (21)     Z ,   -Y ,   -X \t\t(22)    -X ,    Z ,   -Y \t\t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"i 21 3": [' Space Group: I 21 3', ' The lattice is noncentrosymmetric I-centered cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,1/2-Y ,   -Z \t', ' ( 5)    -Z ,1/2+X ,1/2-Y \t( 6) 1/2-Y ,   -Z ,1/2+X \t', ' ( 7) 1/2-Z ,   -X ,1/2+Y \t( 8) 1/2+Y ,1/2-Z ,   -X \t', ' ( 9)    -Y ,1/2+Z ,1/2-X \t(10) 1/2-X ,   -Y ,1/2+Z \t', ' (11) 1/2+Z ,1/2-X ,   -Y \t(12)    -X ,1/2+Y ,1/2-Z \t', ' '] ,
"p 42/m m c": [' Space Group: P 42/m m c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"p 65 2 2": [' Space Group: P 65 2 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,5/6+Z \t', ' ( 3)    -Y ,   X-Y,2/3+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,1/3+Z \t( 6)     Y ,   Y-X,1/6+Z \t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)     X ,   X-Y,5/6-Z \t', ' ( 9)     Y ,    X ,2/3-Z \t(10)    Y-X,    Y ,1/2-Z \t', ' (11)    -X ,   Y-X,1/3-Z \t(12)    -Y ,   -X ,1/6-Z \t', ' '] ,
"p 4/m n c": [' Space Group: P 4/m n c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,1/2+Z \t( 6) 1/2-Y ,1/2-X ,1/2+Z \t', ' ( 7) 1/2+X ,1/2-Y ,1/2+Z \t( 8) 1/2+Y ,1/2+X ,1/2+Z \t', ' '] ,
"c 2/m": [' Space Group: C 2/m', ' The lattice is centrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 8', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,   -Z \t\t', ' '] ,
"f d d d": [' Space Group: F d d d', ' The lattice is centrosymmetric F-centered orthorhombic', ' Multiplicity of a general site is 32', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/4+Y ,1/4+Z \t', ' ( 3) 1/4+X ,   -Y ,1/4+Z \t( 4) 3/4-X ,1/4-Y ,1/2+Z \t', ' '] ,
"c m m 2": [' Space Group: C m m 2', ' The lattice is noncentrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 43 21 2": [' Space Group: P 43 21 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,1/2+X ,3/4+Z \t', ' ( 3)    -X ,   -Y ,1/2+Z \t( 4) 1/2+Y ,1/2-X ,1/4+Z \t', ' ( 5) 1/2-X ,1/2+Y ,3/4-Z \t( 6)    -Y ,   -X ,1/2-Z \t', ' ( 7) 1/2+X ,1/2-Y ,1/4-Z \t( 8)     Y ,    X ,   -Z \t\t', ' '] ,
"p -3 1 m": [' Space Group: P -3 1 m', ' The lattice is centrosymmetric primitive trigonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 31m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,    Z \t\t', ' ( 5)    -X ,   Y-X,    Z \t\t( 6)    X-Y,   -Y ,    Z \t\t', ' '] ,
"i 2 2 2": [' Space Group: I 2 2 2', ' The lattice is noncentrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,   -Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 42/n b c": [' Space Group: P 42/n b c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,1/2+Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,1/2+Z \t', ' ( 5)    -X ,1/2+Y ,    Z \t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7) 1/2+X ,   -Y ,    Z \t( 8) 1/2+Y ,1/2+X ,1/2+Z \t', ' '] ,
"i 4 3 2": [' Space Group: I 4 3 2', ' The lattice is noncentrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)    -Y ,    X ,    Z \t\t', ' ( 5)     Z ,   -Y ,    X \t\t( 6)     X ,    Z ,   -Y \t\t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13)     Y ,   -X ,    Z \t\t(14)     Z ,    Y ,   -X \t\t', ' (15)    -X ,    Z ,    Y \t\t(16)    -X ,   -Z ,   -Y \t\t', ' (17)    -Y ,   -X ,   -Z \t\t(18)    -Z ,   -Y ,   -X \t\t', ' (19)     Y ,   -Z ,   -X \t\t(20)     Y ,    X ,   -Z \t\t', ' (21)    -Z ,    Y ,    X \t\t(22)     X ,   -Z ,    Y \t\t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"p 41 3 2": [' Space Group: P 41 3 2', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/4-Y ,3/4+X ,1/4+Z \t', ' ( 5) 1/4+Z ,1/4-Y ,3/4+X \t( 6) 3/4+X ,1/4+Z ,1/4-Y \t', ' ( 7) 1/2-X ,   -Y ,1/2+Z \t( 8)    -Z ,1/2+X ,1/2-Y \t', ' ( 9) 1/2-Y ,   -Z ,1/2+X \t(10) 1/2+X ,1/2-Y ,   -Z \t', ' (11) 1/2+Z ,1/2-X ,   -Y \t(12)    -Y ,1/2+Z ,1/2-X \t', ' (13) 1/4+Y ,1/4-X ,3/4+Z \t(14) 3/4+Z ,1/4+Y ,1/4-X \t', ' (15) 1/4-X ,3/4+Z ,1/4+Y \t(16) 3/4-X ,3/4-Z ,3/4-Y \t', ' (17) 3/4-Y ,3/4-X ,3/4-Z \t(18) 3/4-Z ,3/4-Y ,3/4-X \t', ' (19) 1/2+Y ,1/2-Z ,   -X \t(20) 3/4+Y ,1/4+X ,1/4-Z \t', ' (21) 1/4-Z ,3/4+Y ,1/4+X \t(22) 1/4+X ,1/4-Z ,3/4+Y \t', ' (23)    -X ,1/2+Y ,1/2-Z \t(24) 1/2-Z ,   -X ,1/2+Y \t', ' '] ,
"p 42/n m c": [' Space Group: P 42/n m c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,1/2+Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,1/2+Z \t', ' ( 5) 1/2-X ,    Y ,    Z \t( 6) 1/2-Y ,1/2-X ,1/2+Z \t', ' ( 7)     X ,1/2-Y ,    Z \t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"p 64 2 2": [' Space Group: P 64 2 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,2/3+Z \t', ' ( 3)    -Y ,   X-Y,1/3+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,2/3+Z \t( 6)     Y ,   Y-X,1/3+Z \t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)     X ,   X-Y,2/3-Z \t', ' ( 9)     Y ,    X ,1/3-Z \t(10)    Y-X,    Y ,   -Z \t\t', ' (11)    -X ,   Y-X,2/3-Z \t(12)    -Y ,   -X ,1/3-Z \t', ' '] ,
"p c a 21": [' Space Group: P c a 21', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,1/2+Z \t', ' ( 3) 1/2+X ,   -Y ,    Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"f d -3 c": [' Space Group: F d -3 c', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 192', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/4+X ,1/4+Y ,   -Z \t', ' ( 5)    -Z ,1/4+X ,1/4+Y \t( 6) 1/4+Y ,   -Z ,1/4+X \t', ' ( 7) 1/4-Z ,1/2+X ,3/4-Y \t( 8) 3/4-Y ,1/4-Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/4-Z ,3/4-X \t(10) 3/4-X ,1/2+Y ,1/4-Z \t', ' (11) 1/4-Z ,3/4-X ,1/2+Y \t(12) 1/2+X ,3/4-Y ,1/4-Z \t', ' (13)     Y ,    X ,1/2+Z \t(14) 1/2+Z ,    Y ,    X \t', ' (15)     X ,1/2+Z ,    Y \t(16) 1/4+Y ,1/4+X ,1/2-Z \t', ' (17) 1/2-Z ,1/4+Y ,1/4+X \t(18) 1/4+X ,1/2-Z ,1/4+Y \t', ' (19) 3/4-Z ,1/2+Y ,3/4-X \t(20) 3/4-X ,3/4-Z ,1/2+Y \t', ' (21) 1/2+X ,3/4-Z ,3/4-Y \t(22) 3/4-Y ,1/2+X ,3/4-Z \t', ' (23) 3/4-Z ,3/4-Y ,1/2+X \t(24) 1/2+Y ,3/4-X ,3/4-Z \t', ' '] ,
"p n a 21": [' Space Group: P n a 21', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,1/2+Z \t', ' ( 3) 1/2+X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"p -4 n 2": [' Space Group: P -4 n 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,1/2+Z \t( 6) 1/2+Y ,1/2+X ,1/2-Z \t', ' ( 7) 1/2+X ,1/2-Y ,1/2+Z \t( 8) 1/2-Y ,1/2-X ,1/2-Z \t', ' '] ,
"p 42/n n m": [' Space Group: P 42/n n m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,1/2+Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,1/2+Z \t', ' ( 5)    -X ,1/2+Y ,1/2+Z \t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7) 1/2+X ,   -Y ,1/2+Z \t( 8) 1/2+Y ,1/2+X ,    Z \t', ' '] ,
"f d -3 m": [' Space Group: F d -3 m', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 192', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/4+X ,1/4+Y ,   -Z \t', ' ( 5)    -Z ,1/4+X ,1/4+Y \t( 6) 1/4+Y ,   -Z ,1/4+X \t', ' ( 7) 1/4-Z ,1/2+X ,3/4-Y \t( 8) 3/4-Y ,1/4-Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/4-Z ,3/4-X \t(10) 3/4-X ,1/2+Y ,1/4-Z \t', ' (11) 1/4-Z ,3/4-X ,1/2+Y \t(12) 1/2+X ,3/4-Y ,1/4-Z \t', ' (13)     Y ,    X ,    Z \t\t(14)     Z ,    Y ,    X \t\t', ' (15)     X ,    Z ,    Y \t\t(16) 1/4+Y ,1/4+X ,   -Z \t', ' (17)    -Z ,1/4+Y ,1/4+X \t(18) 1/4+X ,   -Z ,1/4+Y \t', ' (19) 1/4-Z ,1/2+Y ,3/4-X \t(20) 3/4-X ,1/4-Z ,1/2+Y \t', ' (21) 1/2+X ,1/4-Z ,3/4-Y \t(22) 3/4-Y ,1/2+X ,1/4-Z \t', ' (23) 1/4-Z ,3/4-Y ,1/2+X \t(24) 1/2+Y ,3/4-X ,1/4-Z \t', ' '] ,
"r -3 c r": [' Space Group: R -3 c r', ' The lattice is centrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 12', ' The Laue symmetry is 3mR', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+Y ,1/2+X ,1/2+Z \t', ' ( 5) 1/2+Z ,1/2+Y ,1/2+X \t( 6) 1/2+X ,1/2+Z ,1/2+Y \t', ' '] ,
"p 63 m c": [' Space Group: P 63 m c', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' ( 7)    Y-X,    Y ,    Z \t\t( 8)    -X ,   Y-X,1/2+Z \t', ' ( 9)    -Y ,   -X ,    Z \t\t(10)    X-Y,   -Y ,1/2+Z \t', ' (11)     X ,   X-Y,    Z \t\t(12)     Y ,    X ,1/2+Z \t', ' '] ,
"p 4/m b m": [' Space Group: P 4/m b m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,    Z \t( 6) 1/2-Y ,1/2-X ,    Z \t', ' ( 7) 1/2+X ,1/2-Y ,    Z \t( 8) 1/2+Y ,1/2+X ,    Z \t', ' '] ,
"p 2 2 2": [' Space Group: P 2 2 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,   -Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 63 2 2": [' Space Group: P 63 2 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)     X ,   X-Y,1/2-Z \t', ' ( 9)     Y ,    X ,   -Z \t\t(10)    Y-X,    Y ,1/2-Z \t', ' (11)    -X ,   Y-X,   -Z \t\t(12)    -Y ,   -X ,1/2-Z \t', ' '] ,
"p 6/m m m": [' Space Group: P 6/m m m', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 24', ' The Laue symmetry is 6/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' ( 7)    Y-X,    Y ,    Z \t\t( 8)    -X ,   Y-X,    Z \t\t', ' ( 9)    -Y ,   -X ,    Z \t\t(10)    X-Y,   -Y ,    Z \t\t', ' (11)     X ,   X-Y,    Z \t\t(12)     Y ,    X ,    Z \t\t', ' '] ,
"p c c n": [' Space Group: P c c n', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,1/2+Z \t', ' ( 3)     X ,1/2-Y ,1/2+Z \t( 4) 1/2-X ,1/2-Y ,    Z \t', ' '] ,
"p c c m": [' Space Group: P c c m', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2+Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p m n a": [' Space Group: P m n a', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3) 1/2+X ,   -Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"f 41 3 2": [' Space Group: F 41 3 2', ' The lattice is noncentrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 3/4-Y ,3/4+X ,1/4+Z \t', ' ( 5) 1/4+Z ,3/4-Y ,3/4+X \t( 6) 3/4+X ,1/4+Z ,3/4-Y \t', ' ( 7)    -X ,1/2-Y ,1/2+Z \t( 8) 1/2-Z ,1/2+X ,   -Y \t', ' ( 9)    -Y ,1/2-Z ,1/2+X \t(10) 1/2+X ,   -Y ,1/2-Z \t', ' (11) 1/2+Z ,   -X ,1/2-Y \t(12) 1/2-Y ,1/2+Z ,   -X \t', ' (13) 1/4+Y ,3/4-X ,3/4+Z \t(14) 3/4+Z ,1/4+Y ,3/4-X \t', ' (15) 3/4-X ,3/4+Z ,1/4+Y \t(16) 1/4-X ,1/4-Z ,1/4-Y \t', ' (17) 1/4-Y ,1/4-X ,1/4-Z \t(18) 1/4-Z ,1/4-Y ,1/4-X \t', ' (19) 1/2+Y ,   -Z ,1/2-X \t(20) 3/4+Y ,1/4+X ,3/4-Z \t', ' (21) 3/4-Z ,3/4+Y ,1/4+X \t(22) 1/4+X ,3/4-Z ,3/4+Y \t', ' (23) 1/2-X ,1/2+Y ,   -Z \t(24)    -Z ,1/2-X ,1/2+Y \t', ' '] ,
"r -3 r": [' Space Group: R -3 r', ' The lattice is centrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3R', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t'] ,
"p 1 1 2/m": [' Space Group: P 1 1 2/m', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is c', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 64": [' Space Group: P 64', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,2/3+Z \t', ' ( 3)    -Y ,   X-Y,1/3+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,2/3+Z \t( 6)     Y ,   Y-X,1/3+Z \t', ' '] ,
"p c c a": [' Space Group: P c c a', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,1/2+Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,    Z \t', ' '] ,
"f m -3": [' Space Group: F m -3', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' '] ,
"p -6": [' Space Group: P -6', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    Y-X,   -X ,   -Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)    -Y ,   X-Y,   -Z \t\t', ' '] ,
"i m m m": [' Space Group: I m m m', ' The lattice is centrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p -4 2 m": [' Space Group: P -4 2 m', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)     Y ,    X ,    Z \t\t', ' ( 7)     X ,   -Y ,   -Z \t\t( 8)    -Y ,   -X ,    Z \t\t', ' '] ,
"p 21 3": [' Space Group: P 21 3', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 12', ' The Laue symmetry is m3', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,1/2-Y ,   -Z \t', ' ( 5)    -Z ,1/2+X ,1/2-Y \t( 6) 1/2-Y ,   -Z ,1/2+X \t', ' ( 7) 1/2-Z ,   -X ,1/2+Y \t( 8) 1/2+Y ,1/2-Z ,   -X \t', ' ( 9)    -Y ,1/2+Z ,1/2-X \t(10) 1/2-X ,   -Y ,1/2+Z \t', ' (11) 1/2+Z ,1/2-X ,   -Y \t(12)    -X ,1/2+Y ,1/2-Z \t', ' '] ,
"p 4 m m": [' Space Group: P 4 m m', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"p -4 m 2": [' Space Group: P -4 m 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)     Y ,    X ,   -Z \t\t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)    -Y ,   -X ,   -Z \t\t', ' '] ,
"c 2/c": [' Space Group: C 2/c', ' The lattice is centrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 8', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2-Z \t', ' '] ,
"p 42 3 2": [' Space Group: P 42 3 2', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2-Y ,1/2+X ,1/2+Z \t', ' ( 5) 1/2+Z ,1/2-Y ,1/2+X \t( 6) 1/2+X ,1/2+Z ,1/2-Y \t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13) 1/2+Y ,1/2-X ,1/2+Z \t(14) 1/2+Z ,1/2+Y ,1/2-X \t', ' (15) 1/2-X ,1/2+Z ,1/2+Y \t(16) 1/2-X ,1/2-Z ,1/2-Y \t', ' (17) 1/2-Y ,1/2-X ,1/2-Z \t(18) 1/2-Z ,1/2-Y ,1/2-X \t', ' (19)     Y ,   -Z ,   -X \t\t(20) 1/2+Y ,1/2+X ,1/2-Z \t', ' (21) 1/2-Z ,1/2+Y ,1/2+X \t(22) 1/2+X ,1/2-Z ,1/2+Y \t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"p 6/m c c": [' Space Group: P 6/m c c', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 24', ' The Laue symmetry is 6/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' ( 7)    Y-X,    Y ,1/2+Z \t( 8)    -X ,   Y-X,1/2+Z \t', ' ( 9)    -Y ,   -X ,1/2+Z \t(10)    X-Y,   -Y ,1/2+Z \t', ' (11)     X ,   X-Y,1/2+Z \t(12)     Y ,    X ,1/2+Z \t', ' '] ,
"f m 3": [' Space Group: F m 3', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' '] ,
"p n n a": [' Space Group: P n n a', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,1/2+Z \t', ' ( 3) 1/2+X ,1/2-Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,    Z \t', ' '] ,
"i -4 3 d": [' Space Group: I -4 3 d', ' The lattice is noncentrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 3/4+Y ,1/4-X ,3/4-Z \t', ' ( 5) 3/4-Z ,3/4+Y ,1/4-X \t( 6) 1/4-X ,3/4-Z ,3/4+Y \t', ' ( 7)    -X ,1/2-Y ,    Z \t( 8) 1/2-Z ,    X ,   -Y \t', ' ( 9)    -Y ,1/2-Z ,    X \t(10)     X ,   -Y ,1/2-Z \t', ' (11)     Z ,   -X ,1/2-Y \t(12) 1/2-Y ,    Z ,   -X \t', ' (13) 1/4-Y ,1/4+X ,3/4-Z \t(14) 3/4-Z ,1/4-Y ,1/4+X \t', ' (15) 1/4+X ,3/4-Z ,1/4-Y \t(16) 3/4+X ,3/4+Z ,3/4+Y \t', ' (17) 3/4+Y ,3/4+X ,3/4+Z \t(18) 3/4+Z ,3/4+Y ,3/4+X \t', ' (19) 1/2+Y ,1/2-Z ,   -X \t(20) 3/4-Y ,1/4-X ,1/4+Z \t', ' (21) 1/4+Z ,3/4-Y ,1/4-X \t(22) 1/4-X ,1/4+Z ,3/4-Y \t', ' (23)    -X ,1/2+Y ,1/2-Z \t(24) 1/2-Z ,   -X ,1/2+Y \t', ' '] ,
"p n n n": [' Space Group: P n n n', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,1/2+Z \t', ' ( 3) 1/2+X ,   -Y ,1/2+Z \t( 4) 1/2-X ,1/2-Y ,    Z \t', ' '] ,
"p n n m": [' Space Group: P n n m', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,1/2+Z \t', ' ( 3) 1/2+X ,1/2-Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p -4": [' Space Group: P -4', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 4', ' The Laue symmetry is 4/m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' '] ,
"i -4 3 m": [' Space Group: I -4 3 m', ' The lattice is noncentrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     Y ,   -X ,   -Z \t\t', ' ( 5)    -Z ,    Y ,   -X \t\t( 6)    -X ,   -Z ,    Y \t\t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13)    -Y ,    X ,   -Z \t\t(14)    -Z ,   -Y ,    X \t\t', ' (15)     X ,   -Z ,   -Y \t\t(16)     X ,    Z ,    Y \t\t', ' (17)     Y ,    X ,    Z \t\t(18)     Z ,    Y ,    X \t\t', ' (19)     Y ,   -Z ,   -X \t\t(20)    -Y ,   -X ,    Z \t\t', ' (21)     Z ,   -Y ,   -X \t\t(22)    -X ,    Z ,   -Y \t\t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"p 65": [' Space Group: P 65', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,5/6+Z \t', ' ( 3)    -Y ,   X-Y,2/3+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,1/3+Z \t( 6)     Y ,   Y-X,1/6+Z \t', ' '] ,
"r 3 r": [' Space Group: R 3 r', ' The lattice is noncentrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 3', ' The Laue symmetry is 3R', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t'] ,
"p 2/m 1 1": [' Space Group: P 2/m 1 1', ' The lattice is centrosymmetric primitive monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is a', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' '] ,
"i 41/a": [' Space Group: I 41/a', ' The lattice is centrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 3/4-Y ,1/4+X ,1/4+Z \t', ' ( 3) 1/2-X ,   -Y ,1/2+Z \t( 4) 3/4+Y ,3/4-X ,3/4+Z \t', ' '] ,
"p 63 c m": [' Space Group: P 63 c m', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' ( 7)    Y-X,    Y ,1/2+Z \t( 8)    -X ,   Y-X,    Z \t\t', ' ( 9)    -Y ,   -X ,1/2+Z \t(10)    X-Y,   -Y ,    Z \t\t', ' (11)     X ,   X-Y,1/2+Z \t(12)     Y ,    X ,    Z \t\t', ' '] ,
"c 1 2 1": [' Space Group: C 1 2 1', ' The lattice is noncentrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in y', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,   -Z \t\t', ' '] ,
"p b c n": [' Space Group: P b c n', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4) 1/2-X ,1/2-Y ,1/2+Z \t', ' '] ,
"p b c m": [' Space Group: P b c m', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,    Z \t', ' ( 3)     X ,1/2-Y ,1/2+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"a m m 2": [' Space Group: A m m 2', ' The lattice is noncentrosymmetric A-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"i m -3 m": [' Space Group: I m -3 m', ' The lattice is centrosymmetric I-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' (13)     Y ,    X ,    Z \t\t(14)     Z ,    Y ,    X \t\t', ' (15)     X ,    Z ,    Y \t\t(16)     Y ,    X ,   -Z \t\t', ' (17)    -Z ,    Y ,    X \t\t(18)     X ,   -Z ,    Y \t\t', ' (19)    -Z ,    Y ,   -X \t\t(20)    -X ,   -Z ,    Y \t\t', ' (21)     X ,   -Z ,   -Y \t\t(22)    -Y ,    X ,   -Z \t\t', ' (23)    -Z ,   -Y ,    X \t\t(24)     Y ,   -X ,   -Z \t\t', ' '] ,
"i 4 m m": [' Space Group: I 4 m m', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"p 61 2 2": [' Space Group: P 61 2 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/6+Z \t', ' ( 3)    -Y ,   X-Y,1/3+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,2/3+Z \t( 6)     Y ,   Y-X,5/6+Z \t', ' ( 7)    X-Y,   -Y ,   -Z \t\t( 8)     X ,   X-Y,1/6-Z \t', ' ( 9)     Y ,    X ,1/3-Z \t(10)    Y-X,    Y ,1/2-Z \t', ' (11)    -X ,   Y-X,2/3-Z \t(12)    -Y ,   -X ,5/6-Z \t', ' '] ,
"i m m 2": [' Space Group: I m m 2', ' The lattice is noncentrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 42/n c m": [' Space Group: P 42/n c m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,1/2+Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,1/2+Z \t', ' ( 5) 1/2-X ,    Y ,1/2+Z \t( 6) 1/2-Y ,1/2-X ,    Z \t', ' ( 7)     X ,1/2-Y ,1/2+Z \t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"p b c a": [' Space Group: P b c a', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,    Z \t', ' ( 3)     X ,1/2-Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"p 4 21 2": [' Space Group: P 4 21 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,1/2+X ,    Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4) 1/2+Y ,1/2-X ,    Z \t', ' ( 5) 1/2-X ,1/2+Y ,   -Z \t( 6)    -Y ,   -X ,   -Z \t\t', ' ( 7) 1/2+X ,1/2-Y ,   -Z \t( 8)     Y ,    X ,   -Z \t\t', ' '] ,
"p 4/n n c": [' Space Group: P 4/n n c', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,    X ,    Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4)     Y ,1/2-X ,    Z \t', ' ( 5)    -X ,1/2+Y ,1/2+Z \t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7) 1/2+X ,   -Y ,1/2+Z \t( 8) 1/2+Y ,1/2+X ,1/2+Z \t', ' '] ,
"f m -3 m": [' Space Group: F m -3 m', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 192', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' (13)     Y ,    X ,    Z \t\t(14)     Z ,    Y ,    X \t\t', ' (15)     X ,    Z ,    Y \t\t(16)     Y ,    X ,   -Z \t\t', ' (17)    -Z ,    Y ,    X \t\t(18)     X ,   -Z ,    Y \t\t', ' (19)    -Z ,    Y ,   -X \t\t(20)    -X ,   -Z ,    Y \t\t', ' (21)     X ,   -Z ,   -Y \t\t(22)    -Y ,    X ,   -Z \t\t', ' (23)    -Z ,   -Y ,    X \t\t(24)     Y ,   -X ,   -Z \t\t', ' '] ,
"p 4/m m m": [' Space Group: P 4/m m m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"f m -3 c": [' Space Group: F m -3 c', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 192', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' (13)     Y ,    X ,1/2+Z \t(14) 1/2+Z ,    Y ,    X \t', ' (15)     X ,1/2+Z ,    Y \t(16)     Y ,    X ,1/2-Z \t', ' (17) 1/2-Z ,    Y ,    X \t(18)     X ,1/2-Z ,    Y \t', ' (19) 1/2-Z ,    Y ,   -X \t(20)    -X ,1/2-Z ,    Y \t', ' (21)     X ,1/2-Z ,   -Y \t(22)    -Y ,    X ,1/2-Z \t', ' (23) 1/2-Z ,   -Y ,    X \t(24)     Y ,   -X ,1/2-Z \t', ' '] ,
"p n -3": [' Space Group: P n -3', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,1/2+Y ,   -Z \t', ' ( 5)    -Z ,1/2+X ,1/2+Y \t( 6) 1/2+Y ,   -Z ,1/2+X \t', ' ( 7) 1/2-Z ,    X ,1/2-Y \t( 8) 1/2-Y ,1/2-Z ,    X \t', ' ( 9)     Y ,1/2-Z ,1/2-X \t(10) 1/2-X ,    Y ,1/2-Z \t', ' (11) 1/2-Z ,1/2-X ,    Y \t(12)     X ,1/2-Y ,1/2-Z \t', ' '] ,
"p c c 2": [' Space Group: P c c 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2+Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"i 41 3 2": [' Space Group: I 41 3 2', ' The lattice is noncentrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/4-Y ,3/4+X ,1/4+Z \t', ' ( 5) 1/4+Z ,1/4-Y ,3/4+X \t( 6) 3/4+X ,1/4+Z ,1/4-Y \t', ' ( 7) 1/2-X ,   -Y ,1/2+Z \t( 8)    -Z ,1/2+X ,1/2-Y \t', ' ( 9) 1/2-Y ,   -Z ,1/2+X \t(10) 1/2+X ,1/2-Y ,   -Z \t', ' (11) 1/2+Z ,1/2-X ,   -Y \t(12)    -Y ,1/2+Z ,1/2-X \t', ' (13) 1/4+Y ,1/4-X ,3/4+Z \t(14) 3/4+Z ,1/4+Y ,1/4-X \t', ' (15) 1/4-X ,3/4+Z ,1/4+Y \t(16) 3/4-X ,3/4-Z ,3/4-Y \t', ' (17) 3/4-Y ,3/4-X ,3/4-Z \t(18) 3/4-Z ,3/4-Y ,3/4-X \t', ' (19) 1/2+Y ,1/2-Z ,   -X \t(20) 3/4+Y ,1/4+X ,1/4-Z \t', ' (21) 1/4-Z ,3/4+Y ,1/4+X \t(22) 1/4+X ,1/4-Z ,3/4+Y \t', ' (23)    -X ,1/2+Y ,1/2-Z \t(24) 1/2-Z ,   -X ,1/2+Y \t', ' '] ,
"p 42 m c": [' Space Group: P 42 m c', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"p 4 c c": [' Space Group: P 4 c c', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"p m -3 m": [' Space Group: P m -3 m', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' (13)     Y ,    X ,    Z \t\t(14)     Z ,    Y ,    X \t\t', ' (15)     X ,    Z ,    Y \t\t(16)     Y ,    X ,   -Z \t\t', ' (17)    -Z ,    Y ,    X \t\t(18)     X ,   -Z ,    Y \t\t', ' (19)    -Z ,    Y ,   -X \t\t(20)    -X ,   -Z ,    Y \t\t', ' (21)     X ,   -Z ,   -Y \t\t(22)    -Y ,    X ,   -Z \t\t', ' (23)    -Z ,   -Y ,    X \t\t(24)     Y ,   -X ,   -Z \t\t', ' '] ,
"p 32 1 2": [' Space Group: P 32 1 2', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 31m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,2/3+Z \t', ' ( 3)    Y-X,   -X ,1/3+Z \t( 4)     X ,   X-Y,   -Z \t\t', ' ( 5)    Y-X,    Y ,2/3-Z \t( 6)    -Y ,   -X ,1/3-Z \t', ' '] ,
"p 32 1 1": [' Space Group: P 32 1 1', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 3', ' The Laue symmetry is 3', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,2/3+Z \t', ' ( 3)    Y-X,   -X ,1/3+Z \t'] ,
"r -3 m r": [' Space Group: R -3 m r', ' The lattice is centrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 12', ' The Laue symmetry is 3mR', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     Y ,    X ,    Z \t\t', ' ( 5)     Z ,    Y ,    X \t\t( 6)     X ,    Z ,    Y \t\t', ' '] ,
"p 3 c 1": [' Space Group: P 3 c 1', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3m1', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,1/2+Z \t', ' ( 5)    -Y ,   -X ,1/2+Z \t( 6)     X ,   X-Y,1/2+Z \t', ' '] ,
"p 2 2 21": [' Space Group: P 2 2 21', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,1/2-Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"p 63": [' Space Group: P 63', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/2+Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,1/2+Z \t', ' '] ,
"p m 3": [' Space Group: P m 3', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' '] ,
"p 42/m": [' Space Group: P 42/m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' '] ,
"p m c 21": [' Space Group: P m c 21', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,    Z \t\t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"p 42/n": [' Space Group: P 42/n', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,1/2+X ,1/2+Z \t', ' ( 3) 1/2-X ,1/2-Y ,    Z \t( 4) 1/2+Y ,   -X ,1/2+Z \t', ' '] ,
"a m a 2": [' Space Group: A m a 2', ' The lattice is noncentrosymmetric A-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,    Z \t', ' ( 3) 1/2+X ,   -Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 6/m": [' Space Group: P 6/m', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' '] ,
"p -6 c 2": [' Space Group: P -6 c 2', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    Y-X,   -X ,1/2-Z \t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)     X ,    Y ,1/2-Z \t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)    -Y ,   X-Y,1/2-Z \t', ' ( 7)    Y-X,    Y ,1/2+Z \t( 8)     X ,   X-Y,   -Z \t\t', ' ( 9)    -Y ,   -X ,1/2+Z \t(10)    Y-X,    Y ,   -Z \t\t', ' (11)     X ,   X-Y,1/2+Z \t(12)    -Y ,   -X ,   -Z \t\t', ' '] ,
"i -4 c 2": [' Space Group: I -4 c 2', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)     Y ,    X ,1/2-Z \t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)    -Y ,   -X ,1/2-Z \t', ' '] ,
"F -1": [' Space Group: F -1', ' The lattice is centrosymmetric F-centered triclinic', ' Multiplicity of a general site is 8', ' The Laue symmetry is -1', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t'] ,
"p 3 1 m": [' Space Group: P 3 1 m', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 31m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,    Z \t\t', ' ( 5)    -X ,   Y-X,    Z \t\t( 6)    X-Y,   -Y ,    Z \t\t', ' '] ,
"c c c 2": [' Space Group: C c c 2', ' The lattice is noncentrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2+Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"i m 3": [' Space Group: I m 3', ' The lattice is centrosymmetric I-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,    Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,    Y \t\t( 6)     Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,    X ,   -Y \t\t( 8)    -Y ,   -Z ,    X \t\t', ' ( 9)     Y ,   -Z ,   -X \t\t(10)    -X ,    Y ,   -Z \t\t', ' (11)    -Z ,   -X ,    Y \t\t(12)     X ,   -Y ,   -Z \t\t', ' '] ,
"p -4 3 m": [' Space Group: P -4 3 m', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     Y ,   -X ,   -Z \t\t', ' ( 5)    -Z ,    Y ,   -X \t\t( 6)    -X ,   -Z ,    Y \t\t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13)    -Y ,    X ,   -Z \t\t(14)    -Z ,   -Y ,    X \t\t', ' (15)     X ,   -Z ,   -Y \t\t(16)     X ,    Z ,    Y \t\t', ' (17)     Y ,    X ,    Z \t\t(18)     Z ,    Y ,    X \t\t', ' (19)     Y ,   -Z ,   -X \t\t(20)    -Y ,   -X ,    Z \t\t', ' (21)     Z ,   -Y ,   -X \t\t(22)    -X ,    Z ,   -Y \t\t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"p -4 3 n": [' Space Group: P -4 3 n', ' The lattice is noncentrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+Y ,1/2-X ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+Y ,1/2-X \t( 6) 1/2-X ,1/2-Z ,1/2+Y \t', ' ( 7)    -X ,   -Y ,    Z \t\t( 8)    -Z ,    X ,   -Y \t\t', ' ( 9)    -Y ,   -Z ,    X \t\t(10)     X ,   -Y ,   -Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -Y ,    Z ,   -X \t\t', ' (13) 1/2-Y ,1/2+X ,1/2-Z \t(14) 1/2-Z ,1/2-Y ,1/2+X \t', ' (15) 1/2+X ,1/2-Z ,1/2-Y \t(16) 1/2+X ,1/2+Z ,1/2+Y \t', ' (17) 1/2+Y ,1/2+X ,1/2+Z \t(18) 1/2+Z ,1/2+Y ,1/2+X \t', ' (19)     Y ,   -Z ,   -X \t\t(20) 1/2-Y ,1/2-X ,1/2+Z \t', ' (21) 1/2+Z ,1/2-Y ,1/2-X \t(22) 1/2-X ,1/2+Z ,1/2-Y \t', ' (23)    -X ,    Y ,   -Z \t\t(24)    -Z ,   -X ,    Y \t\t', ' '] ,
"p -3 1 c": [' Space Group: P -3 1 c', ' The lattice is centrosymmetric primitive trigonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 31m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,1/2+Z \t', ' ( 5)    -X ,   Y-X,1/2+Z \t( 6)    X-Y,   -Y ,1/2+Z \t', ' '] ,
"r 3 m": [' Space Group: R 3 m', ' The lattice is noncentrosymmetric R-centered trigonal', ' Multiplicity of a general site is 18', ' The Laue symmetry is 3m1', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,    Z \t\t', ' ( 5)    -Y ,   -X ,    Z \t\t( 6)     X ,   X-Y,    Z \t\t', ' '] ,
"p 21": [' Space Group: P 21', ' The lattice is noncentrosymmetric primitive monoclinic', ' Multiplicity of a general site is 2', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in y', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,   -Z \t', ' '] ,
"r -3": [' Space Group: R -3', ' The lattice is centrosymmetric R-centered trigonal', ' Multiplicity of a general site is 18', ' The Laue symmetry is 3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t'] ,
"c m": [' Space Group: C m', ' The lattice is noncentrosymmetric C-centered monoclinic', ' Multiplicity of a general site is 4', ' The Laue symmetry is 2/m', ' The unique monoclinic axis is b', ' The location of the origin is arbitrary in x z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,    Z \t\t', ' '] ,
"p 32 2 1": [' Space Group: P 32 2 1', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3m1', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,2/3+Z \t', ' ( 3)    Y-X,   -X ,1/3+Z \t( 4)     Y ,    X ,   -Z \t\t', ' ( 5)    -X ,   Y-X,2/3-Z \t( 6)    X-Y,   -Y ,1/3-Z \t', ' '] ,
"i 21 21 21": [' Space Group: I 21 21 21', ' The lattice is noncentrosymmetric I-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2+X ,1/2-Y ,   -Z \t', ' ( 3)    -X ,1/2+Y ,1/2-Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"p 42 2 2": [' Space Group: P 42 2 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)    -Y ,   -X ,1/2-Z \t', ' ( 7)     X ,   -Y ,   -Z \t\t( 8)     Y ,    X ,1/2-Z \t', ' '] ,
"i -4 2 m": [' Space Group: I -4 2 m', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)     Y ,    X ,    Z \t\t', ' ( 7)     X ,   -Y ,   -Z \t\t( 8)    -Y ,   -X ,    Z \t\t', ' '] ,
"p 65 1 1": [' Space Group: P 65 1 1', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,5/6+Z \t', ' ( 3)    -Y ,   X-Y,2/3+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,1/3+Z \t( 6)     Y ,   Y-X,1/6+Z \t', ' '] ,
"p 61": [' Space Group: P 61', ' The lattice is noncentrosymmetric primitive hexagonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 6/m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,1/6+Z \t', ' ( 3)    -Y ,   X-Y,1/3+Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' ( 5)    Y-X,   -X ,2/3+Z \t( 6)     Y ,   Y-X,5/6+Z \t', ' '] ,
"i 2 3": [' Space Group: I 2 3', ' The lattice is noncentrosymmetric I-centered cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,   -Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,   -Y \t\t( 6)    -Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,   -X ,    Y \t\t( 8)     Y ,   -Z ,   -X \t\t', ' ( 9)    -Y ,    Z ,   -X \t\t(10)    -X ,   -Y ,    Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -X ,    Y ,   -Z \t\t', ' '] ,
"i -4 2 d": [' Space Group: I -4 2 d', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5) 1/2-X ,    Y ,3/4-Z \t( 6)     Y ,1/2+X ,1/4+Z \t', ' ( 7) 1/2+X ,   -Y ,3/4-Z \t( 8)    -Y ,1/2-X ,1/4+Z \t', ' '] ,
"p a 3": [' Space Group: P a 3', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 24', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,    Y ,1/2-Z \t', ' ( 5) 1/2-Z ,1/2+X ,    Y \t( 6)     Y ,1/2-Z ,1/2+X \t', ' ( 7)    -Z ,1/2+X ,1/2-Y \t( 8) 1/2-Y ,   -Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/2-Z ,   -X \t(10)    -X ,1/2+Y ,1/2-Z \t', ' (11) 1/2-Z ,   -X ,1/2+Y \t(12) 1/2+X ,1/2-Y ,   -Z \t', ' '] ,
"f 2 3": [' Space Group: F 2 3', ' The lattice is noncentrosymmetric F-centered cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     X ,   -Y ,   -Z \t\t', ' ( 5)    -Z ,    X ,   -Y \t\t( 6)    -Y ,   -Z ,    X \t\t', ' ( 7)    -Z ,   -X ,    Y \t\t( 8)     Y ,   -Z ,   -X \t\t', ' ( 9)    -Y ,    Z ,   -X \t\t(10)    -X ,   -Y ,    Z \t\t', ' (11)     Z ,   -X ,   -Y \t\t(12)    -X ,    Y ,   -Z \t\t', ' '] ,
"i 4 c m": [' Space Group: I 4 c m', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,   -X ,1/2+Z \t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)     Y ,    X ,1/2+Z \t', ' '] ,
"r 3 c": [' Space Group: R 3 c', ' The lattice is noncentrosymmetric R-centered trigonal', ' Multiplicity of a general site is 18', ' The Laue symmetry is 3m1', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,1/2+Z \t', ' ( 5)    -Y ,   -X ,1/2+Z \t( 6)     X ,   X-Y,1/2+Z \t', ' '] ,
"p n m a": [' Space Group: P n m a', ' The lattice is centrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,1/2+Y ,1/2+Z \t', ' ( 3)     X ,1/2-Y ,    Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"r 3 c r": [' Space Group: R 3 c r', ' The lattice is noncentrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3mR', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+Y ,1/2+X ,1/2+Z \t', ' ( 5) 1/2+Z ,1/2+Y ,1/2+X \t( 6) 1/2+X ,1/2+Z ,1/2+Y \t', ' '] ,
"p n c 2": [' Space Group: P n c 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,1/2+Z \t', ' ( 3)     X ,1/2-Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"c 2 2 21": [' Space Group: C 2 2 21', ' The lattice is noncentrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,1/2-Z \t( 4)    -X ,   -Y ,1/2+Z \t', ' '] ,
"r 3 m r": [' Space Group: R 3 m r', ' The lattice is noncentrosymmetric primitive rhombohedral', ' Multiplicity of a general site is 6', ' The Laue symmetry is 3mR', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4)     Y ,    X ,    Z \t\t', ' ( 5)     Z ,    Y ,    X \t\t( 6)     X ,    Z ,    Y \t\t', ' '] ,
"p 43 2 2": [' Space Group: P 43 2 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,3/4+Z \t', ' ( 3)    -X ,   -Y ,1/2+Z \t( 4)     Y ,   -X ,1/4+Z \t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)    -Y ,   -X ,3/4-Z \t', ' ( 7)     X ,   -Y ,1/2-Z \t( 8)     Y ,    X ,1/4-Z \t', ' '] ,
"r 3 2": [' Space Group: R 3 2', ' The lattice is noncentrosymmetric R-centered trigonal', ' Multiplicity of a general site is 18', ' The Laue symmetry is 3m1', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,   -Z \t\t', ' ( 5)    -X ,   Y-X,   -Z \t\t( 6)    X-Y,   -Y ,   -Z \t\t', ' '] ,
"p m a 2": [' Space Group: P m a 2', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,    Z \t', ' ( 3) 1/2+X ,   -Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"i 4/m m m": [' Space Group: I 4/m m m', ' The lattice is centrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 32', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,    Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,    Z \t\t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7)     X ,   -Y ,    Z \t\t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"c c c a": [' Space Group: C c c a', ' The lattice is centrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-X ,    Y ,1/2+Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4) 1/2-X ,   -Y ,    Z \t', ' '] ,
"i 41 m d": [' Space Group: I 41 m d', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,1/2+X ,1/4+Z \t', ' ( 3) 1/2-X ,1/2-Y ,1/2+Z \t( 4) 1/2+Y ,   -X ,3/4+Z \t', ' ( 5)    -X ,    Y ,    Z \t\t( 6)    -Y ,1/2-X ,1/4+Z \t', ' ( 7) 1/2+X ,1/2-Y ,1/2+Z \t( 8) 1/2+Y ,    X ,3/4+Z \t', ' '] ,
"c c c m": [' Space Group: C c c m', ' The lattice is centrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 16', ' The Laue symmetry is mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,    Y ,1/2+Z \t', ' ( 3)     X ,   -Y ,1/2+Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p 41 21 2": [' Space Group: P 41 21 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,1/2+X ,1/4+Z \t', ' ( 3)    -X ,   -Y ,1/2+Z \t( 4) 1/2+Y ,1/2-X ,3/4+Z \t', ' ( 5) 1/2-X ,1/2+Y ,1/4-Z \t( 6)    -Y ,   -X ,1/2-Z \t', ' ( 7) 1/2+X ,1/2-Y ,3/4-Z \t( 8)     Y ,    X ,   -Z \t\t', ' '] ,
"p 31": [' Space Group: P 31', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 3', ' The Laue symmetry is 3', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,1/3+Z \t', ' ( 3)    Y-X,   -X ,2/3+Z \t'] ,
"p 32": [' Space Group: P 32', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 3', ' The Laue symmetry is 3', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,2/3+Z \t', ' ( 3)    Y-X,   -X ,1/3+Z \t'] ,
"p 42/m n m": [' Space Group: P 42/m n m', ' The lattice is centrosymmetric primitive tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2-Y ,1/2+X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4) 1/2+Y ,1/2-X ,1/2+Z \t', ' ( 5) 1/2-X ,1/2+Y ,1/2+Z \t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7) 1/2+X ,1/2-Y ,1/2+Z \t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"p 3 1 2": [' Space Group: P 3 1 2', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 31m', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     X ,   X-Y,   -Z \t\t', ' ( 5)    Y-X,    Y ,   -Z \t\t( 6)    -Y ,   -X ,   -Z \t\t', ' '] ,
"i 41 2 2": [' Space Group: I 41 2 2', ' The lattice is noncentrosymmetric I-centered tetragonal', ' Multiplicity of a general site is 16', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,1/2+X ,1/4+Z \t', ' ( 3) 1/2-X ,1/2-Y ,1/2+Z \t( 4) 1/2+Y ,   -X ,3/4+Z \t', ' ( 5) 1/2-X ,    Y ,3/4-Z \t( 6)    -Y ,   -X ,   -Z \t\t', ' ( 7)     X ,1/2-Y ,1/4-Z \t( 8) 1/2+Y ,1/2+X ,1/2-Z \t', ' '] ,
"p -3 m 1": [' Space Group: P -3 m 1', ' The lattice is centrosymmetric primitive trigonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 3m1', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)    Y-X,    Y ,    Z \t\t', ' ( 5)    -Y ,   -X ,    Z \t\t( 6)     X ,   X-Y,    Z \t\t', ' '] ,
"a b m 2": [' Space Group: A b m 2', ' The lattice is noncentrosymmetric A-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -X ,1/2+Y ,    Z \t', ' ( 3)     X ,1/2-Y ,    Z \t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p n -3 n": [' Space Group: P n -3 n', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,1/2+Y ,   -Z \t', ' ( 5)    -Z ,1/2+X ,1/2+Y \t( 6) 1/2+Y ,   -Z ,1/2+X \t', ' ( 7) 1/2-Z ,    X ,1/2-Y \t( 8) 1/2-Y ,1/2-Z ,    X \t', ' ( 9)     Y ,1/2-Z ,1/2-X \t(10) 1/2-X ,    Y ,1/2-Z \t', ' (11) 1/2-Z ,1/2-X ,    Y \t(12)     X ,1/2-Y ,1/2-Z \t', ' (13) 1/2+Y ,1/2+X ,1/2+Z \t(14) 1/2+Z ,1/2+Y ,1/2+X \t', ' (15) 1/2+X ,1/2+Z ,1/2+Y \t(16)     Y ,    X ,1/2-Z \t', ' (17) 1/2-Z ,    Y ,    X \t(18)     X ,1/2-Z ,    Y \t', ' (19)    -Z ,1/2+Y ,   -X \t(20)    -X ,   -Z ,1/2+Y \t', ' (21) 1/2+X ,   -Z ,   -Y \t(22)    -Y ,1/2+X ,   -Z \t', ' (23)    -Z ,   -Y ,1/2+X \t(24) 1/2+Y ,   -X ,   -Z \t', ' '] ,
"r 3": [' Space Group: R 3', ' The lattice is noncentrosymmetric R-centered trigonal', ' Multiplicity of a general site is 9', ' The Laue symmetry is 3', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t'] ,
"c 2 2 2": [' Space Group: C 2 2 2', ' The lattice is noncentrosymmetric C-centered orthorhombic', ' Multiplicity of a general site is 8', ' The Laue symmetry is mmm', '\n The equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     X ,   -Y ,   -Z \t\t', ' ( 3)    -X ,    Y ,   -Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' '] ,
"p n -3 m": [' Space Group: P n -3 m', ' The lattice is centrosymmetric primitive cubic', ' Multiplicity of a general site is 48', ' The Laue symmetry is m3m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/2+X ,1/2+Y ,   -Z \t', ' ( 5)    -Z ,1/2+X ,1/2+Y \t( 6) 1/2+Y ,   -Z ,1/2+X \t', ' ( 7) 1/2-Z ,    X ,1/2-Y \t( 8) 1/2-Y ,1/2-Z ,    X \t', ' ( 9)     Y ,1/2-Z ,1/2-X \t(10) 1/2-X ,    Y ,1/2-Z \t', ' (11) 1/2-Z ,1/2-X ,    Y \t(12)     X ,1/2-Y ,1/2-Z \t', ' (13)     Y ,    X ,    Z \t\t(14)     Z ,    Y ,    X \t\t', ' (15)     X ,    Z ,    Y \t\t(16) 1/2+Y ,1/2+X ,   -Z \t', ' (17)    -Z ,1/2+Y ,1/2+X \t(18) 1/2+X ,   -Z ,1/2+Y \t', ' (19) 1/2-Z ,    Y ,1/2-X \t(20) 1/2-X ,1/2-Z ,    Y \t', ' (21)     X ,1/2-Z ,1/2-Y \t(22) 1/2-Y ,    X ,1/2-Z \t', ' (23) 1/2-Z ,1/2-Y ,    X \t(24)     Y ,1/2-X ,1/2-Z \t', ' '] ,
"p 42 c m": [' Space Group: P 42 c m', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/2+Z \t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)     Y ,   -X ,1/2+Z \t', ' ( 5)    -X ,    Y ,1/2+Z \t( 6)    -Y ,   -X ,    Z \t\t', ' ( 7)     X ,   -Y ,1/2+Z \t( 8)     Y ,    X ,    Z \t\t', ' '] ,
"p 6/m 1 1": [' Space Group: P 6/m 1 1', ' The lattice is centrosymmetric primitive hexagonal', ' Multiplicity of a general site is 12', ' The Laue symmetry is 6/m', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    X-Y,    X ,    Z \t\t', ' ( 3)    -Y ,   X-Y,    Z \t\t( 4)    -X ,   -Y ,    Z \t\t', ' ( 5)    Y-X,   -X ,    Z \t\t( 6)     Y ,   Y-X,    Z \t\t', ' '] ,
"p 21 21 21": [' Space Group: P 21 21 21', ' The lattice is noncentrosymmetric primitive orthorhombic', ' Multiplicity of a general site is 4', ' The Laue symmetry is mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2) 1/2+X ,1/2-Y ,   -Z \t', ' ( 3)    -X ,1/2+Y ,1/2-Z \t( 4) 1/2-X ,   -Y ,1/2+Z \t', ' '] ,
"f d -3": [' Space Group: F d -3', ' The lattice is centrosymmetric F-centered cubic', ' Multiplicity of a general site is 96', ' The Laue symmetry is m3', ' The inversion center is located at 0,0,0', '\n The equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+\n', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Z ,    X ,    Y \t\t', ' ( 3)     Y ,    Z ,    X \t\t( 4) 1/4+X ,1/4+Y ,   -Z \t', ' ( 5)    -Z ,1/4+X ,1/4+Y \t( 6) 1/4+Y ,   -Z ,1/4+X \t', ' ( 7) 1/4-Z ,1/2+X ,3/4-Y \t( 8) 3/4-Y ,1/4-Z ,1/2+X \t', ' ( 9) 1/2+Y ,1/4-Z ,3/4-X \t(10) 3/4-X ,1/2+Y ,1/4-Z \t', ' (11) 1/4-Z ,3/4-X ,1/2+Y \t(12) 1/2+X ,3/4-Y ,1/4-Z \t', ' '] ,
"p -4 b 2": [' Space Group: P -4 b 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)     Y ,   -X ,   -Z \t\t', ' ( 3)    -X ,   -Y ,    Z \t\t( 4)    -Y ,    X ,   -Z \t\t', ' ( 5) 1/2-X ,1/2+Y ,    Z \t( 6) 1/2+Y ,1/2+X ,   -Z \t', ' ( 7) 1/2+X ,1/2-Y ,    Z \t( 8) 1/2-Y ,1/2-X ,   -Z \t', ' '] ,
"p 3 1 c": [' Space Group: P 3 1 c', ' The lattice is noncentrosymmetric primitive trigonal', ' Multiplicity of a general site is 6', ' The Laue symmetry is 31m', ' The location of the origin is arbitrary in z', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,   X-Y,    Z \t\t', ' ( 3)    Y-X,   -X ,    Z \t\t( 4)     Y ,    X ,1/2+Z \t', ' ( 5)    -X ,   Y-X,1/2+Z \t( 6)    X-Y,   -Y ,1/2+Z \t', ' '] ,
"p 41 2 2": [' Space Group: P 41 2 2', ' The lattice is noncentrosymmetric primitive tetragonal', ' Multiplicity of a general site is 8', ' The Laue symmetry is 4/mmm', '\n The equivalent positions are:', ' ( 1)     X ,    Y ,    Z \t\t( 2)    -Y ,    X ,1/4+Z \t', ' ( 3)    -X ,   -Y ,1/2+Z \t( 4)     Y ,   -X ,3/4+Z \t', ' ( 5)    -X ,    Y ,   -Z \t\t( 6)    -Y ,   -X ,1/4-Z \t', ' ( 7)     X ,   -Y ,1/2-Z \t( 8)     Y ,    X ,3/4-Z \t', ' '] ,
}
