# output from GSASIIspc computed on platform darwin on 2010-02-18 import numpy as np array = np.array float32=np.float32 SGdat = { "p 4/n b m": {'SGCen': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0], [0.33333333333333331, 0.66666666666666663, 0.66666666666666663], [0.66666666666666663, 0.33333333333333331, 0.33333333333333331]], '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': [[0, 0, 0]], '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': [[0, 0, 0], [0, 0.5, 0.5]], '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': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0], [0.5, 0.5, 0.5]], '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': [[0, 0, 0]], '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 b a 2": {'SGCen': [[0, 0, 0]], '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': [[0, 0, 0], [0.5, 0.5, 0.5]], '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': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0], [0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]], '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.], [ 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., 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., 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., 0., 0.], dtype=float32)], [array([[ 0., 0., -1.], [ 0., -1., 0.], [-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([[ 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)]]} , "p -4 21 m": {'SGCen': [[0, 0, 0]], 'SGLatt': 'P', 'SpGrp': 'P -4 21 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.], 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 63/m c m": {'SGCen': [[0, 0, 0]], 'SGLatt': 'P', 'SpGrp': 'P 63/m c m', 'SGLaue': '6/mmm', 'SGSys': 'hexagonal', 'SGInv': True, 'SGUniq': '', 'SGOps': [[array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]], dtype=float32), array([ 0., 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[ 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)]]} , "c 2 2 2": {'SGCen': [[0, 0, 0], [0.5, 0.5, 0]], 'SGLatt': 'C', 'SpGrp': 'C 2 2 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., 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)]]} , "p n -3 m": {'SGCen': [[0, 0, 0]], 'SGLatt': 'P', 'SpGrp': 'P n -3 m', 'SGLaue': 'm3m', '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([ 0.5, 0.5, 0. ], dtype=float32)], [array([[ 0., 0., -1.], [ 1., 0., 0.], [ 0., 1., 0.]], dtype=float32), array([ 0. , 0.5, 0.5], dtype=float32)], [array([[ 0., 1., 0.], [ 0., 0., -1.], [ 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 32 2 1": {'SGCen': [[0, 0, 0]], 'SGLatt': 'P', 'SpGrp': 'P 32 2 1', '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.], [ 1., -1., 0.], [ 0., 0., 1.]], dtype=float32), array([ 0. , 0. , 0.66666669], dtype=float32)], [array([[-1., 1., 0.], [-1., 0., 0.], [ 0., 0., 1.]], dtype=float32), array([ 0. , 0. , 0.33333334], 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. , 0.66666669], dtype=float32)], [array([[ 1., -1., 0.], [ 0., -1., 0.], [ 0., 0., -1.]], dtype=float32), array([ 0. , 0. , 0.33333334], dtype=float32)]]} , "p 6/m 1 1": {'SGCen': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0], [0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0]], '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': [[0, 0, 0]], '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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X , Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X , Z ', '( 5) -X ,1/2+Y , Z ( 6) -Y , -X , Z ', '( 7) 1/2+X , -Y , Z ( 8) 1/2+Y ,1/2+X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y ,1/2+Z ( 6) Y , X ,1/2-Z ', '( 7) X , -Y ,1/2+Z ( 8) -Y , -X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y , Z ( 5) -Y , -X , Z ( 6) X , X-Y, Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y ,1/2+X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) 1/2+Y ,1/2-X ,1/2+Z ', '( 5) 1/2-X ,1/2+Y ,1/2+Z ( 6) -Y , -X , Z ', '( 7) 1/2+X ,1/2-Y ,1/2+Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) 1/2+X ,1/2-Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z ', '( 5) 1/2-X ,1/2+Y , Z ( 6) 1/2-Y ,1/2-X ,1/2+Z ', '( 7) 1/2+X ,1/2-Y , Z ( 8) 1/2+Y ,1/2+X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) 1/2+X , -Y ,1/2+Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y ,1/2+Z ( 6) -Y , -X ,1/2+Z ', '( 7) X , -Y ,1/2+Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z ', '( 5) -X , Y ,1/2+Z ( 6) -Y , -X , Z ', '( 7) X , -Y ,1/2+Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) 1/2+X ,1/2-Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) 1/2+X ,1/2-Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/4+Z ', '( 3) -X , -Y ,1/2+Z ( 4) Y , -X ,3/4+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,3/4+Z ', '( 3) -X , -Y ,1/2+Z ( 4) Y , -X ,1/4+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) -Y , X , Z ( 5) Z , -Y , X ( 6) X , Z , -Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) Y , -X , Z (14) Z , Y , -X (15) -X , Z , Y ', '(16) -X , -Z , -Y (17) -Y , -X , -Z (18) -Z , -Y , -X ', '(19) Y , -Z , -X (20) Y , X , -Z (21) -Z , Y , X ', '(22) X , -Z , Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) 1/2-X ,1/2+Y , -Z ( 6) 1/2+Y ,1/2+X , Z ', '( 7) 1/2+X ,1/2-Y , -Z ( 8) 1/2-Y ,1/2-X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z ', '( 7) Y-X, Y ,1/2+Z ( 8) -X , Y-X, Z ( 9) -Y , -X ,1/2+Z ', '(10) X-Y, -Y , Z (11) X , X-Y,1/2+Z (12) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , -Y , -Z ( 5) -Z , X , -Y ( 6) -Y , -Z , X ', '( 7) -Z , -X , Y ( 8) Y , -Z , -X ( 9) -Y , Z , -X ', '(10) -X , -Y , Z (11) Z , -X , -Y (12) -X , Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X , Y ,1/2-Z ( 5) 1/2-Z ,1/2+X , Y ( 6) Y ,1/2-Z ,1/2+X ', '( 7) -Z ,1/2+X ,1/2-Y ( 8) 1/2-Y , -Z ,1/2+X ( 9) 1/2+Y ,1/2-Z , -X ', '(10) -X ,1/2+Y ,1/2-Z (11) 1/2-Z , -X ,1/2+Y (12) 1/2+X ,1/2-Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y , X , -Z ( 5) -X , Y-X, -Z ( 6) X-Y, -Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X , Y ,1/2-Z ( 5) 1/2-Z ,1/2+X , Y ( 6) Y ,1/2-Z ,1/2+X ', '( 7) -Z ,1/2+X ,1/2-Y ( 8) 1/2-Y , -Z ,1/2+X ( 9) 1/2+Y ,1/2-Z , -X ', '(10) -X ,1/2+Y ,1/2-Z (11) 1/2-Z , -X ,1/2+Y (12) 1/2+X ,1/2-Y , -Z ', '(13) 1/4+Y ,1/4+X ,1/4+Z (14) 1/4+Z ,1/4+Y ,1/4+X (15) 1/4+X ,1/4+Z ,1/4+Y ', '(16) 3/4+Y ,1/4+X ,1/4-Z (17) 1/4-Z ,3/4+Y ,1/4+X (18) 1/4+X ,1/4-Z ,3/4+Y ', '(19) 3/4-Z ,3/4+Y ,1/4-X (20) 1/4-X ,3/4-Z ,3/4+Y (21) 3/4+X ,1/4-Z ,3/4-Y ', '(22) 3/4-Y ,3/4+X ,1/4-Z (23) 1/4-Z ,3/4-Y ,3/4+X (24) 3/4+Y ,1/4-X ,3/4-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z ', '( 7) X-Y, -Y , -Z ( 8) X , X-Y,1/2-Z ( 9) Y , X , -Z ', '(10) Y-X, Y ,1/2-Z (11) -X , Y-X, -Z (12) -Y , -X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y , X , -Z ( 5) -X , Y-X, -Z ( 6) X-Y, -Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y , -Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z ', '( 7) Y-X, Y ,1/2+Z ( 8) -X , Y-X,1/2+Z ( 9) -Y , -X ,1/2+Z ', '(10) X-Y, -Y ,1/2+Z (11) X , X-Y,1/2+Z (12) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) -Y , -X , -Z ( 5) -Z , -Y , -X ( 6) -X , -Z , -Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/3+Z ( 3) -Y , X-Y,2/3+Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X ,1/3+Z ( 6) Y , Y-X,2/3+Z ', '( 7) X-Y, -Y , -Z ( 8) X , X-Y,1/3-Z ( 9) Y , X ,2/3-Z ', '(10) Y-X, Y , -Z (11) -X , Y-X,1/3-Z (12) -Y , -X ,2/3-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y ,1/2+X ,1/4+Z ', '( 3) 1/2-X ,1/2-Y ,1/2+Z ( 4) 1/2+Y , -X ,3/4+Z ', '( 5) -X , Y ,1/2+Z ( 6) -Y ,1/2-X ,3/4+Z ', '( 7) 1/2+X ,1/2-Y , Z ( 8) 1/2+Y , X ,1/4+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y , -Z ( 6) -Y , -X , -Z ', '( 7) X , -Y , -Z ( 8) Y , X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y,1/3+Z ( 3) Y-X, -X ,2/3+Z ', '( 4) Y , X , -Z ( 5) -X , Y-X,1/3-Z ( 6) X-Y, -Y ,2/3-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2+X ,1/2-Y , -Z ', '( 3) 1/2-X ,1/2+Y , -Z ( 4) -X , -Y , Z '] , "i 41 1 1": ['Space Group I 41 1 1', 'The lattice is noncentrosymmetric I-centered tetragonal', 'Multiplicity of a general site is 8', 'The Laue symmetry is 4/mmm', 'The location of the origin is arbitrary in z', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y ,1/2+X ,1/4+Z ', '( 3) 1/2-X ,1/2-Y ,1/2+Z ( 4) 1/2+Y , -X ,3/4+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) 1/2+X ,1/2-Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) 1/2+X ,1/2-Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y , Z ', '( 3) 1/2+X , -Y , Z ( 4) 1/2-X ,1/2-Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z ', '(13) 1/2+Y ,1/2+X ,1/2+Z (14) 1/2+Z ,1/2+Y ,1/2+X (15) 1/2+X ,1/2+Z ,1/2+Y ', '(16) 1/2+Y ,1/2+X ,1/2-Z (17) 1/2-Z ,1/2+Y ,1/2+X (18) 1/2+X ,1/2-Z ,1/2+Y ', '(19) 1/2-Z ,1/2+Y ,1/2-X (20) 1/2-X ,1/2-Z ,1/2+Y (21) 1/2+X ,1/2-Z ,1/2-Y ', '(22) 1/2-Y ,1/2+X ,1/2-Z (23) 1/2-Z ,1/2-Y ,1/2+X (24) 1/2+Y ,1/2-X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) X ,1/2-Y ,1/2+Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y ,1/2+X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) 1/2+Y ,1/2-X ,1/2+Z ', '( 5) 1/2-X ,1/2+Y ,1/2-Z ( 6) -Y , -X , -Z ', '( 7) 1/2+X ,1/2-Y ,1/2-Z ( 8) Y , X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X , Y , Z ', '( 3) X ,1/2-Y , Z ( 4) 1/2-X ,1/2-Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z ', '( 5) 1/2-X ,1/2+Y , Z ( 6) 1/2-Y ,1/2-X ,1/2+Z ', '( 7) 1/2+X ,1/2-Y , Z ( 8) 1/2+Y ,1/2+X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X , Y , Z ', '( 3) X , -Y , Z ( 4) 1/2-X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y , Z ( 6) Y , X , -Z ', '( 7) X , -Y , Z ( 8) -Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) 1/2-X ,1/2+Y ,1/2-Z ( 6) 1/2+Y ,1/2+X ,1/2+Z ', '( 7) 1/2+X ,1/2-Y ,1/2-Z ( 8) 1/2-Y ,1/2-X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y , -Z ( 6) -Y , -X , -Z ', '( 7) X , -Y , -Z ( 8) Y , X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y ,1/2+Z ( 6) -Y , -X ,1/2+Z ', '( 7) X , -Y ,1/2+Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y-X, -X , -Z ( 3) -Y , X-Y, Z ', '( 4) X , Y , -Z ( 5) Y-X, -X , Z ( 6) -Y , X-Y, -Z ', '( 7) X-Y, -Y , -Z ( 8) -X , Y-X, Z ( 9) Y , X , -Z ', '(10) X-Y, -Y , Z (11) -X , Y-X, -Z (12) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y-X, -X ,1/2-Z ( 3) -Y , X-Y, Z ', '( 4) X , Y ,1/2-Z ( 5) Y-X, -X , Z ( 6) -Y , X-Y,1/2-Z ', '( 7) X-Y, -Y , -Z ( 8) -X , Y-X,1/2+Z ( 9) Y , X , -Z ', '(10) X-Y, -Y ,1/2+Z (11) -X , Y-X, -Z (12) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z ', '( 7) Y-X, Y , Z ( 8) -X , Y-X, Z ( 9) -Y , -X , Z ', '(10) X-Y, -Y , Z (11) X , X-Y, Z (12) Y , X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 3/4-Y ,1/4+X ,3/4+Z ( 5) 3/4+Z ,3/4-Y ,1/4+X ( 6) 1/4+X ,3/4+Z ,3/4-Y ', '( 7) 1/2-X , -Y ,1/2+Z ( 8) -Z ,1/2+X ,1/2-Y ( 9) 1/2-Y , -Z ,1/2+X ', '(10) 1/2+X ,1/2-Y , -Z (11) 1/2+Z ,1/2-X , -Y (12) -Y ,1/2+Z ,1/2-X ', '(13) 3/4+Y ,3/4-X ,1/4+Z (14) 1/4+Z ,3/4+Y ,3/4-X (15) 3/4-X ,1/4+Z ,3/4+Y ', '(16) 1/4-X ,1/4-Z ,1/4-Y (17) 1/4-Y ,1/4-X ,1/4-Z (18) 1/4-Z ,1/4-Y ,1/4-X ', '(19) 1/2+Y ,1/2-Z , -X (20) 1/4+Y ,3/4+X ,3/4-Z (21) 3/4-Z ,1/4+Y ,3/4+X ', '(22) 3/4+X ,3/4-Z ,1/4+Y (23) -X ,1/2+Y ,1/2-Z (24) 1/2-Z , -X ,1/2+Y '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y , -Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) 1/4-X ,1/4+Y ,1/4+Z ', '( 3) 1/4+X ,1/4-Y ,1/4+Z ( 4) -X ,1/2-Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/3+Z ( 3) -Y , X-Y,2/3+Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X ,1/3+Z ( 6) Y , Y-X,2/3+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X ,1/2-Y , Z ( 4) -X ,1/2-Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y ,1/2+Z ( 5) -Y , -X ,1/2+Z ( 6) X , X-Y,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X ,1/2-Y ,1/2+Z ( 4) -X ,1/2-Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2-X , Y , Z ', '( 3) 1/2+X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z ', '( 7) Y-X, Y , Z ( 8) -X , Y-X,1/2+Z ( 9) -Y , -X , Z ', '(10) X-Y, -Y ,1/2+Z (11) X , X-Y, Z (12) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) -Y , X , Z ( 5) Z , -Y , X ( 6) X , Z , -Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) Y , -X , Z (14) Z , Y , -X (15) -X , Z , Y ', '(16) -X , -Z , -Y (17) -Y , -X , -Z (18) -Z , -Y , -X ', '(19) Y , -Z , -X (20) Y , X , -Z (21) -Z , Y , X ', '(22) X , -Z , Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/4-Y ,3/4+X ,1/4+Z ', '( 3) 1/2-X , -Y ,1/2+Z ( 4) 1/4+Y ,1/4-X ,3/4+Z ', '( 5) -X , Y ,1/2+Z ( 6) 1/4-Y ,3/4-X ,3/4+Z ', '( 7) 1/2+X , -Y , Z ( 8) 1/4+Y ,1/4+X ,1/4+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y ,1/2-Z ( 6) Y , X ,1/2+Z ', '( 7) X , -Y ,1/2-Z ( 8) -Y , -X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) 1/2-X ,1/2+Y ,1/2+Z ( 6) 1/2-Y ,1/2-X ,1/2+Z ', '( 7) 1/2+X ,1/2-Y ,1/2+Z ( 8) 1/2+Y ,1/2+X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X , Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y ,1/2+Z ( 5) -Y , -X ,1/2+Z ( 6) X , X-Y,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X , Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X , Z ', '( 5) 1/2-X , Y , Z ( 6) 1/2-Y ,1/2-X , Z ', '( 7) X ,1/2-Y , Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y , Z ( 5) -Y , -X , Z ( 6) X , X-Y, Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z ', '( 7) X-Y, -Y , -Z ( 8) X , X-Y, -Z ( 9) Y , X , -Z ', '(10) Y-X, Y , -Z (11) -X , Y-X, -Z (12) -Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/4-Y ,3/4+X ,1/4+Z ', '( 3) 1/2-X , -Y ,1/2+Z ( 4) 1/4+Y ,1/4-X ,3/4+Z ', '( 5) -X , Y , Z ( 6) 1/4-Y ,3/4-X ,1/4+Z ', '( 7) 1/2+X , -Y ,1/2+Z ( 8) 1/4+Y ,1/4+X ,3/4+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X , Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X , Z ', '( 5) 1/2-X , Y ,1/2+Z ( 6) 1/2-Y ,1/2-X ,1/2+Z ', '( 7) X ,1/2-Y ,1/2+Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X ,1/2-Y , Z ( 4) -X ,1/2-Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) 1/2-X ,1/2+Y , Z ( 6) 1/2-Y ,1/2-X , Z ', '( 7) 1/2+X ,1/2-Y , Z ( 8) 1/2+Y ,1/2+X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y-X, -X , -Z ( 3) -Y , X-Y, Z ', '( 4) X , Y , -Z ( 5) Y-X, -X , Z ( 6) -Y , X-Y, -Z ', '( 7) Y-X, Y , Z ( 8) X , X-Y, -Z ( 9) -Y , -X , Z ', '(10) Y-X, Y , -Z (11) X , X-Y, Z (12) -Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y ,1/2+Z ', '( 3) 1/2+X ,1/2-Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y,1/3+Z ( 3) Y-X, -X ,2/3+Z ', '( 4) X , X-Y, -Z ( 5) Y-X, Y ,1/3-Z ( 6) -Y , -X ,2/3-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+Y ,1/2-X ,1/2-Z ( 5) 1/2-Z ,1/2+Y ,1/2-X ( 6) 1/2-X ,1/2-Z ,1/2+Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) 1/2-Y ,1/2+X ,1/2-Z (14) 1/2-Z ,1/2-Y ,1/2+X (15) 1/2+X ,1/2-Z ,1/2-Y ', '(16) 1/2+X ,1/2+Z ,1/2+Y (17) 1/2+Y ,1/2+X ,1/2+Z (18) 1/2+Z ,1/2+Y ,1/2+X ', '(19) Y , -Z , -X (20) 1/2-Y ,1/2-X ,1/2+Z (21) 1/2+Z ,1/2-Y ,1/2-X ', '(22) 1/2-X ,1/2+Z ,1/2-Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) Y , -X , -Z ( 5) -Z , Y , -X ( 6) -X , -Z , Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) -Y , X , -Z (14) -Z , -Y , X (15) X , -Z , -Y ', '(16) X , Z , Y (17) Y , X , Z (18) Z , Y , X ', '(19) Y , -Z , -X (20) -Y , -X , Z (21) Z , -Y , -X ', '(22) -X , Z , -Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X ,1/2-Y , -Z ( 5) -Z ,1/2+X ,1/2-Y ( 6) 1/2-Y , -Z ,1/2+X ', '( 7) 1/2-Z , -X ,1/2+Y ( 8) 1/2+Y ,1/2-Z , -X ( 9) -Y ,1/2+Z ,1/2-X ', '(10) 1/2-X , -Y ,1/2+Z (11) 1/2+Z ,1/2-X , -Y (12) -X ,1/2+Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z ', '( 5) -X , Y , Z ( 6) -Y , -X ,1/2+Z ', '( 7) X , -Y , Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,5/6+Z ( 3) -Y , X-Y,2/3+Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X ,1/3+Z ( 6) Y , Y-X,1/6+Z ', '( 7) X-Y, -Y , -Z ( 8) X , X-Y,5/6-Z ( 9) Y , X ,2/3-Z ', '(10) Y-X, Y ,1/2-Z (11) -X , Y-X,1/3-Z (12) -Y , -X ,1/6-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) 1/2-X ,1/2+Y ,1/2+Z ( 6) 1/2-Y ,1/2-X ,1/2+Z ', '( 7) 1/2+X ,1/2-Y ,1/2+Z ( 8) 1/2+Y ,1/2+X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X ,1/4+Y ,1/4+Z ', '( 3) 1/4+X , -Y ,1/4+Z ( 4) 3/4-X ,1/4-Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y ,1/2+X ,3/4+Z ', '( 3) -X , -Y ,1/2+Z ( 4) 1/2+Y ,1/2-X ,1/4+Z ', '( 5) 1/2-X ,1/2+Y ,3/4-Z ( 6) -Y , -X ,1/2-Z ', '( 7) 1/2+X ,1/2-Y ,1/4-Z ( 8) Y , X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y , X , Z ( 5) -X , Y-X, Z ( 6) X-Y, -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y , -Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X ,1/2+Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X ,1/2+Z ', '( 5) -X ,1/2+Y , Z ( 6) -Y , -X ,1/2+Z ', '( 7) 1/2+X , -Y , Z ( 8) 1/2+Y ,1/2+X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) -Y , X , Z ( 5) Z , -Y , X ( 6) X , Z , -Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) Y , -X , Z (14) Z , Y , -X (15) -X , Z , Y ', '(16) -X , -Z , -Y (17) -Y , -X , -Z (18) -Z , -Y , -X ', '(19) Y , -Z , -X (20) Y , X , -Z (21) -Z , Y , X ', '(22) X , -Z , Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/4-Y ,3/4+X ,1/4+Z ( 5) 1/4+Z ,1/4-Y ,3/4+X ( 6) 3/4+X ,1/4+Z ,1/4-Y ', '( 7) 1/2-X , -Y ,1/2+Z ( 8) -Z ,1/2+X ,1/2-Y ( 9) 1/2-Y , -Z ,1/2+X ', '(10) 1/2+X ,1/2-Y , -Z (11) 1/2+Z ,1/2-X , -Y (12) -Y ,1/2+Z ,1/2-X ', '(13) 1/4+Y ,1/4-X ,3/4+Z (14) 3/4+Z ,1/4+Y ,1/4-X (15) 1/4-X ,3/4+Z ,1/4+Y ', '(16) 3/4-X ,3/4-Z ,3/4-Y (17) 3/4-Y ,3/4-X ,3/4-Z (18) 3/4-Z ,3/4-Y ,3/4-X ', '(19) 1/2+Y ,1/2-Z , -X (20) 3/4+Y ,1/4+X ,1/4-Z (21) 1/4-Z ,3/4+Y ,1/4+X ', '(22) 1/4+X ,1/4-Z ,3/4+Y (23) -X ,1/2+Y ,1/2-Z (24) 1/2-Z , -X ,1/2+Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X ,1/2+Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X ,1/2+Z ', '( 5) 1/2-X , Y , Z ( 6) 1/2-Y ,1/2-X ,1/2+Z ', '( 7) X ,1/2-Y , Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,2/3+Z ( 3) -Y , X-Y,1/3+Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X ,2/3+Z ( 6) Y , Y-X,1/3+Z ', '( 7) X-Y, -Y , -Z ( 8) X , X-Y,2/3-Z ( 9) Y , X ,1/3-Z ', '(10) Y-X, Y , -Z (11) -X , Y-X,2/3-Z (12) -Y , -X ,1/3-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X , Y ,1/2+Z ', '( 3) 1/2+X , -Y , Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/4+X ,1/4+Y , -Z ( 5) -Z ,1/4+X ,1/4+Y ( 6) 1/4+Y , -Z ,1/4+X ', '( 7) 1/4-Z ,1/2+X ,3/4-Y ( 8) 3/4-Y ,1/4-Z ,1/2+X ( 9) 1/2+Y ,1/4-Z ,3/4-X ', '(10) 3/4-X ,1/2+Y ,1/4-Z (11) 1/4-Z ,3/4-X ,1/2+Y (12) 1/2+X ,3/4-Y ,1/4-Z ', '(13) Y , X ,1/2+Z (14) 1/2+Z , Y , X (15) X ,1/2+Z , Y ', '(16) 1/4+Y ,1/4+X ,1/2-Z (17) 1/2-Z ,1/4+Y ,1/4+X (18) 1/4+X ,1/2-Z ,1/4+Y ', '(19) 3/4-Z ,1/2+Y ,3/4-X (20) 3/4-X ,3/4-Z ,1/2+Y (21) 1/2+X ,3/4-Z ,3/4-Y ', '(22) 3/4-Y ,1/2+X ,3/4-Z (23) 3/4-Z ,3/4-Y ,1/2+X (24) 1/2+Y ,3/4-X ,3/4-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y ,1/2+Z ', '( 3) 1/2+X ,1/2-Y , Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) 1/2-X ,1/2+Y ,1/2+Z ( 6) 1/2+Y ,1/2+X ,1/2-Z ', '( 7) 1/2+X ,1/2-Y ,1/2+Z ( 8) 1/2-Y ,1/2-X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X ,1/2+Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X ,1/2+Z ', '( 5) -X ,1/2+Y ,1/2+Z ( 6) -Y , -X , Z ', '( 7) 1/2+X , -Y ,1/2+Z ( 8) 1/2+Y ,1/2+X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/4+X ,1/4+Y , -Z ( 5) -Z ,1/4+X ,1/4+Y ( 6) 1/4+Y , -Z ,1/4+X ', '( 7) 1/4-Z ,1/2+X ,3/4-Y ( 8) 3/4-Y ,1/4-Z ,1/2+X ( 9) 1/2+Y ,1/4-Z ,3/4-X ', '(10) 3/4-X ,1/2+Y ,1/4-Z (11) 1/4-Z ,3/4-X ,1/2+Y (12) 1/2+X ,3/4-Y ,1/4-Z ', '(13) Y , X , Z (14) Z , Y , X (15) X , Z , Y ', '(16) 1/4+Y ,1/4+X , -Z (17) -Z ,1/4+Y ,1/4+X (18) 1/4+X , -Z ,1/4+Y ', '(19) 1/4-Z ,1/2+Y ,3/4-X (20) 3/4-X ,1/4-Z ,1/2+Y (21) 1/2+X ,1/4-Z ,3/4-Y ', '(22) 3/4-Y ,1/2+X ,1/4-Z (23) 1/4-Z ,3/4-Y ,1/2+X (24) 1/2+Y ,3/4-X ,1/4-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+Y ,1/2+X ,1/2+Z ( 5) 1/2+Z ,1/2+Y ,1/2+X ( 6) 1/2+X ,1/2+Z ,1/2+Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z ', '( 7) Y-X, Y , Z ( 8) -X , Y-X,1/2+Z ( 9) -Y , -X , Z ', '(10) X-Y, -Y ,1/2+Z (11) X , X-Y, Z (12) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) 1/2-X ,1/2+Y , Z ( 6) 1/2-Y ,1/2-X , Z ', '( 7) 1/2+X ,1/2-Y , Z ( 8) 1/2+Y ,1/2+X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y , -Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z ', '( 7) Y-X, Y , Z ( 8) -X , Y-X, Z ( 9) -Y , -X , Z ', '(10) X-Y, -Y , Z (11) X , X-Y, Z (12) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X , Y ,1/2+Z ', '( 3) X ,1/2-Y ,1/2+Z ( 4) 1/2-X ,1/2-Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y ,1/2+Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) 1/2+X , -Y ,1/2+Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 3/4-Y ,3/4+X ,1/4+Z ( 5) 1/4+Z ,3/4-Y ,3/4+X ( 6) 3/4+X ,1/4+Z ,3/4-Y ', '( 7) -X ,1/2-Y ,1/2+Z ( 8) 1/2-Z ,1/2+X , -Y ( 9) -Y ,1/2-Z ,1/2+X ', '(10) 1/2+X , -Y ,1/2-Z (11) 1/2+Z , -X ,1/2-Y (12) 1/2-Y ,1/2+Z , -X ', '(13) 1/4+Y ,3/4-X ,3/4+Z (14) 3/4+Z ,1/4+Y ,3/4-X (15) 3/4-X ,3/4+Z ,1/4+Y ', '(16) 1/4-X ,1/4-Z ,1/4-Y (17) 1/4-Y ,1/4-X ,1/4-Z (18) 1/4-Z ,1/4-Y ,1/4-X ', '(19) 1/2+Y , -Z ,1/2-X (20) 3/4+Y ,1/4+X ,3/4-Z (21) 3/4-Z ,3/4+Y ,1/4+X ', '(22) 1/4+X ,3/4-Z ,3/4+Y (23) 1/2-X ,1/2+Y , -Z (24) -Z ,1/2-X ,1/2+Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,2/3+Z ( 3) -Y , X-Y,1/3+Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X ,2/3+Z ( 6) Y , Y-X,1/3+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X , Y ,1/2+Z ', '( 3) X , -Y ,1/2+Z ( 4) 1/2-X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y-X, -X , -Z ( 3) -Y , X-Y, Z ', '( 4) X , Y , -Z ( 5) Y-X, -X , Z ( 6) -Y , X-Y, -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y , -Z ( 6) Y , X , Z ', '( 7) X , -Y , -Z ( 8) -Y , -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X ,1/2-Y , -Z ( 5) -Z ,1/2+X ,1/2-Y ( 6) 1/2-Y , -Z ,1/2+X ', '( 7) 1/2-Z , -X ,1/2+Y ( 8) 1/2+Y ,1/2-Z , -X ( 9) -Y ,1/2+Z ,1/2-X ', '(10) 1/2-X , -Y ,1/2+Z (11) 1/2+Z ,1/2-X , -Y (12) -X ,1/2+Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y , Z ( 6) -Y , -X , Z ', '( 7) X , -Y , Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y , Z ( 6) Y , X , -Z ', '( 7) X , -Y , Z ( 8) -Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2-Y ,1/2+X ,1/2+Z ( 5) 1/2+Z ,1/2-Y ,1/2+X ( 6) 1/2+X ,1/2+Z ,1/2-Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) 1/2+Y ,1/2-X ,1/2+Z (14) 1/2+Z ,1/2+Y ,1/2-X (15) 1/2-X ,1/2+Z ,1/2+Y ', '(16) 1/2-X ,1/2-Z ,1/2-Y (17) 1/2-Y ,1/2-X ,1/2-Z (18) 1/2-Z ,1/2-Y ,1/2-X ', '(19) Y , -Z , -X (20) 1/2+Y ,1/2+X ,1/2-Z (21) 1/2-Z ,1/2+Y ,1/2+X ', '(22) 1/2+X ,1/2-Z ,1/2+Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z ', '( 7) Y-X, Y ,1/2+Z ( 8) -X , Y-X,1/2+Z ( 9) -Y , -X ,1/2+Z ', '(10) X-Y, -Y ,1/2+Z (11) X , X-Y,1/2+Z (12) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y ,1/2+Z ', '( 3) 1/2+X ,1/2-Y ,1/2+Z ( 4) 1/2-X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 3/4+Y ,1/4-X ,3/4-Z ( 5) 3/4-Z ,3/4+Y ,1/4-X ( 6) 1/4-X ,3/4-Z ,3/4+Y ', '( 7) -X ,1/2-Y , Z ( 8) 1/2-Z , X , -Y ( 9) -Y ,1/2-Z , X ', '(10) X , -Y ,1/2-Z (11) Z , -X ,1/2-Y (12) 1/2-Y , Z , -X ', '(13) 1/4-Y ,1/4+X ,3/4-Z (14) 3/4-Z ,1/4-Y ,1/4+X (15) 1/4+X ,3/4-Z ,1/4-Y ', '(16) 3/4+X ,3/4+Z ,3/4+Y (17) 3/4+Y ,3/4+X ,3/4+Z (18) 3/4+Z ,3/4+Y ,3/4+X ', '(19) 1/2+Y ,1/2-Z , -X (20) 3/4-Y ,1/4-X ,1/4+Z (21) 1/4+Z ,3/4-Y ,1/4-X ', '(22) 1/4-X ,1/4+Z ,3/4-Y (23) -X ,1/2+Y ,1/2-Z (24) 1/2-Z , -X ,1/2+Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y ,1/2+Z ', '( 3) 1/2+X , -Y ,1/2+Z ( 4) 1/2-X ,1/2-Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y ,1/2+Z ', '( 3) 1/2+X ,1/2-Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) Y , -X , -Z ( 5) -Z , Y , -X ( 6) -X , -Z , Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) -Y , X , -Z (14) -Z , -Y , X (15) X , -Z , -Y ', '(16) X , Z , Y (17) Y , X , Z (18) Z , Y , X ', '(19) Y , -Z , -X (20) -Y , -X , Z (21) Z , -Y , -X ', '(22) -X , Z , -Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y ,1/2+Z ( 5) -Y , -X ,1/2+Z ( 6) X , X-Y,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X , -Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 3/4-Y ,1/4+X ,1/4+Z ', '( 3) 1/2-X , -Y ,1/2+Z ( 4) 3/4+Y ,3/4-X ,3/4+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) X , -Y ,1/2+Z ( 4) 1/2-X ,1/2-Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y , Z ', '( 3) X ,1/2-Y ,1/2+Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z ', '(13) Y , X , Z (14) Z , Y , X (15) X , Z , Y ', '(16) Y , X , -Z (17) -Z , Y , X (18) X , -Z , Y ', '(19) -Z , Y , -X (20) -X , -Z , Y (21) X , -Z , -Y ', '(22) -Y , X , -Z (23) -Z , -Y , X (24) Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y , Z ( 6) -Y , -X , Z ', '( 7) X , -Y , Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/6+Z ( 3) -Y , X-Y,1/3+Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X ,2/3+Z ( 6) Y , Y-X,5/6+Z ', '( 7) X-Y, -Y , -Z ( 8) X , X-Y,1/6-Z ( 9) Y , X ,1/3-Z ', '(10) Y-X, Y ,1/2-Z (11) -X , Y-X,2/3-Z (12) -Y , -X ,5/6-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X ,1/2+Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X ,1/2+Z ', '( 5) 1/2-X , Y ,1/2+Z ( 6) 1/2-Y ,1/2-X , Z ', '( 7) X ,1/2-Y ,1/2+Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y , Z ', '( 3) X ,1/2-Y ,1/2+Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y ,1/2+X , Z ', '( 3) -X , -Y , Z ( 4) 1/2+Y ,1/2-X , Z ', '( 5) 1/2-X ,1/2+Y , -Z ( 6) -Y , -X , -Z ', '( 7) 1/2+X ,1/2-Y , -Z ( 8) Y , X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y , X , Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) Y ,1/2-X , Z ', '( 5) -X ,1/2+Y ,1/2+Z ( 6) -Y , -X ,1/2+Z ', '( 7) 1/2+X , -Y ,1/2+Z ( 8) 1/2+Y ,1/2+X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z ', '(13) Y , X , Z (14) Z , Y , X (15) X , Z , Y ', '(16) Y , X , -Z (17) -Z , Y , X (18) X , -Z , Y ', '(19) -Z , Y , -X (20) -X , -Z , Y (21) X , -Z , -Y ', '(22) -Y , X , -Z (23) -Z , -Y , X (24) Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y , Z ( 6) -Y , -X , Z ', '( 7) X , -Y , Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z ', '(13) Y , X ,1/2+Z (14) 1/2+Z , Y , X (15) X ,1/2+Z , Y ', '(16) Y , X ,1/2-Z (17) 1/2-Z , Y , X (18) X ,1/2-Z , Y ', '(19) 1/2-Z , Y , -X (20) -X ,1/2-Z , Y (21) X ,1/2-Z , -Y ', '(22) -Y , X ,1/2-Z (23) 1/2-Z , -Y , X (24) Y , -X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X ,1/2+Y , -Z ( 5) -Z ,1/2+X ,1/2+Y ( 6) 1/2+Y , -Z ,1/2+X ', '( 7) 1/2-Z , X ,1/2-Y ( 8) 1/2-Y ,1/2-Z , X ( 9) Y ,1/2-Z ,1/2-X ', '(10) 1/2-X , Y ,1/2-Z (11) 1/2-Z ,1/2-X , Y (12) X ,1/2-Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y ,1/2+Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/4-Y ,3/4+X ,1/4+Z ( 5) 1/4+Z ,1/4-Y ,3/4+X ( 6) 3/4+X ,1/4+Z ,1/4-Y ', '( 7) 1/2-X , -Y ,1/2+Z ( 8) -Z ,1/2+X ,1/2-Y ( 9) 1/2-Y , -Z ,1/2+X ', '(10) 1/2+X ,1/2-Y , -Z (11) 1/2+Z ,1/2-X , -Y (12) -Y ,1/2+Z ,1/2-X ', '(13) 1/4+Y ,1/4-X ,3/4+Z (14) 3/4+Z ,1/4+Y ,1/4-X (15) 1/4-X ,3/4+Z ,1/4+Y ', '(16) 3/4-X ,3/4-Z ,3/4-Y (17) 3/4-Y ,3/4-X ,3/4-Z (18) 3/4-Z ,3/4-Y ,3/4-X ', '(19) 1/2+Y ,1/2-Z , -X (20) 3/4+Y ,1/4+X ,1/4-Z (21) 1/4-Z ,3/4+Y ,1/4+X ', '(22) 1/4+X ,1/4-Z ,3/4+Y (23) -X ,1/2+Y ,1/2-Z (24) 1/2-Z , -X ,1/2+Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z ', '( 5) -X , Y , Z ( 6) -Y , -X ,1/2+Z ', '( 7) X , -Y , Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y ,1/2+Z ( 6) -Y , -X ,1/2+Z ', '( 7) X , -Y ,1/2+Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z ', '(13) Y , X , Z (14) Z , Y , X (15) X , Z , Y ', '(16) Y , X , -Z (17) -Z , Y , X (18) X , -Z , Y ', '(19) -Z , Y , -X (20) -X , -Z , Y (21) X , -Z , -Y ', '(22) -Y , X , -Z (23) -Z , -Y , X (24) Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y,2/3+Z ( 3) Y-X, -X ,1/3+Z ', '( 4) X , X-Y, -Z ( 5) Y-X, Y ,2/3-Z ( 6) -Y , -X ,1/3-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y,2/3+Z ( 3) Y-X, -X ,1/3+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) Y , X , Z ( 5) Z , Y , X ( 6) X , Z , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y ,1/2+Z ( 5) -Y , -X ,1/2+Z ( 6) X , X-Y,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y ,1/2-Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , Y , -Z ( 5) -Z , X , Y ( 6) Y , -Z , X ', '( 7) -Z , X , -Y ( 8) -Y , -Z , X ( 9) Y , -Z , -X ', '(10) -X , Y , -Z (11) -Z , -X , Y (12) X , -Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X , Y , Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y ,1/2+Z '] , "c 2 1 1": ['Space Group C 2 1 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 a', 'The location of the origin is arbitrary in x', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) X , -Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y ,1/2+X ,1/2+Z ', '( 3) 1/2-X ,1/2-Y , Z ( 4) 1/2+Y , -X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2-X , Y , Z ', '( 3) 1/2+X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y-X, -X ,1/2-Z ( 3) -Y , X-Y, Z ', '( 4) X , Y ,1/2-Z ( 5) Y-X, -X , Z ( 6) -Y , X-Y,1/2-Z ', '( 7) Y-X, Y ,1/2+Z ( 8) X , X-Y, -Z ( 9) -Y , -X ,1/2+Z ', '(10) Y-X, Y , -Z (11) X , X-Y,1/2+Z (12) -Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y ,1/2+Z ( 6) Y , X ,1/2-Z ', '( 7) X , -Y ,1/2+Z ( 8) -Y , -X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y ,1/2+Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) Y , -X , -Z ( 5) -Z , Y , -X ( 6) -X , -Z , Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) -Y , X , -Z (14) -Z , -Y , X (15) X , -Z , -Y ', '(16) X , Z , Y (17) Y , X , Z (18) Z , Y , X ', '(19) Y , -Z , -X (20) -Y , -X , Z (21) Z , -Y , -X ', '(22) -X , Z , -Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+Y ,1/2-X ,1/2-Z ( 5) 1/2-Z ,1/2+Y ,1/2-X ( 6) 1/2-X ,1/2-Z ,1/2+Y ', '( 7) -X , -Y , Z ( 8) -Z , X , -Y ( 9) -Y , -Z , X ', '(10) X , -Y , -Z (11) Z , -X , -Y (12) -Y , Z , -X ', '(13) 1/2-Y ,1/2+X ,1/2-Z (14) 1/2-Z ,1/2-Y ,1/2+X (15) 1/2+X ,1/2-Z ,1/2-Y ', '(16) 1/2+X ,1/2+Z ,1/2+Y (17) 1/2+Y ,1/2+X ,1/2+Z (18) 1/2+Z ,1/2+Y ,1/2+X ', '(19) Y , -Z , -X (20) 1/2-Y ,1/2-X ,1/2+Z (21) 1/2+Z ,1/2-Y ,1/2-X ', '(22) 1/2-X ,1/2+Z ,1/2-Y (23) -X , Y , -Z (24) -Z , -X , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y , X ,1/2+Z ( 5) -X , Y-X,1/2+Z ( 6) X-Y, -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,3/4+Z ', '( 3) -X , -Y ,1/2+Z ( 4) Y , -X ,1/4+Z ', '( 5) -X , Y , -Z ( 6) -Y , -X ,3/4-Z ', '( 7) X , -Y ,1/2-Z ( 8) Y , X ,1/4-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y , X , Z ( 5) -X , Y-X, Z ( 6) X-Y, -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) 1/2+X ,1/2-Y , -Z ', '( 3) -X ,1/2+Y ,1/2-Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) Y , -X ,1/2+Z ', '( 5) -X , Y , -Z ( 6) -Y , -X ,1/2-Z ', '( 7) X , -Y , -Z ( 8) Y , X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) -X , Y , -Z ( 6) Y , X , Z ', '( 7) X , -Y , -Z ( 8) -Y , -X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,5/6+Z ( 3) -Y , X-Y,2/3+Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X ,1/3+Z ( 6) Y , Y-X,1/6+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/6+Z ( 3) -Y , X-Y,1/3+Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X ,2/3+Z ( 6) Y , Y-X,5/6+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , -Y , -Z ( 5) -Z , X , -Y ( 6) -Y , -Z , X ', '( 7) -Z , -X , Y ( 8) Y , -Z , -X ( 9) -Y , Z , -X ', '(10) -X , -Y , Z (11) Z , -X , -Y (12) -X , Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) 1/2-X , Y ,3/4-Z ( 6) Y ,1/2+X ,1/4+Z ', '( 7) 1/2+X , -Y ,3/4-Z ( 8) -Y ,1/2-X ,1/4+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X , Y ,1/2-Z ( 5) 1/2-Z ,1/2+X , Y ( 6) Y ,1/2-Z ,1/2+X ', '( 7) -Z ,1/2+X ,1/2-Y ( 8) 1/2-Y , -Z ,1/2+X ( 9) 1/2+Y ,1/2-Z , -X ', '(10) -X ,1/2+Y ,1/2-Z (11) 1/2-Z , -X ,1/2+Y (12) 1/2+X ,1/2-Y , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) X , -Y , -Z ( 5) -Z , X , -Y ( 6) -Y , -Z , X ', '( 7) -Z , -X , Y ( 8) Y , -Z , -X ( 9) -Y , Z , -X ', '(10) -X , -Y , Z (11) Z , -X , -Y (12) -X , Y , -Z '] , "p 2 c m": ['Space Group P 2 c m', '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 x', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) X , -Y ,1/2+Z ( 4) X , Y ,1/2-Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y ,1/2+Z ( 6) -Y , -X ,1/2+Z ', '( 7) X , -Y ,1/2+Z ( 8) Y , X ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y , Z ( 5) -Y , -X , Z ( 6) X , X-Y, Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X ,1/2+Y ,1/2+Z ', '( 3) X ,1/2-Y , Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+Y ,1/2+X ,1/2+Z ( 5) 1/2+Z ,1/2+Y ,1/2+X ( 6) 1/2+X ,1/2+Z ,1/2+Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y ,1/2+Z ', '( 3) X ,1/2-Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y ,1/2-Z ( 4) -X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) Y , X , Z ( 5) Z , Y , X ( 6) X , Z , Y '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-X , Y , Z ', '( 3) 1/2+X , -Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y , X , Z ', '( 3) -X , -Y , Z ( 4) Y , -X , Z ', '( 5) -X , Y , Z ( 6) -Y , -X , Z ', '( 7) X , -Y , Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) 1/2-X , Y ,1/2+Z ', '( 3) X , -Y ,1/2+Z ( 4) 1/2-X , -Y , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y ,1/2+X ,1/4+Z ', '( 3) 1/2-X ,1/2-Y ,1/2+Z ( 4) 1/2+Y , -X ,3/4+Z ', '( 5) -X , Y , Z ( 6) -Y ,1/2-X ,1/4+Z ', '( 7) 1/2+X ,1/2-Y ,1/2+Z ( 8) 1/2+Y , X ,3/4+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) -X , Y ,1/2+Z ', '( 3) X , -Y ,1/2+Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y ,1/2+X ,1/4+Z ', '( 3) -X , -Y ,1/2+Z ( 4) 1/2+Y ,1/2-X ,3/4+Z ', '( 5) 1/2-X ,1/2+Y ,1/4-Z ( 6) -Y , -X ,1/2-Z ', '( 7) 1/2+X ,1/2-Y ,3/4-Z ( 8) Y , X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y,1/3+Z ( 3) Y-X, -X ,2/3+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X ,1/2+Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y ,1/2+Z ( 5) Y-X, -X , Z ( 6) Y , Y-X,1/2+Z ', '( 7) Y-X, Y ,1/2+Z ( 8) -X , Y-X, Z ( 9) -Y , -X ,1/2+Z ', '(10) X-Y, -Y , Z (11) X , X-Y,1/2+Z (12) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2-Y ,1/2+X ,1/2+Z ', '( 3) -X , -Y , Z ( 4) 1/2+Y ,1/2-X ,1/2+Z ', '( 5) 1/2-X ,1/2+Y ,1/2+Z ( 6) -Y , -X , Z ', '( 7) 1/2+X ,1/2-Y ,1/2+Z ( 8) Y , X , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) X , X-Y, -Z ( 5) Y-X, Y , -Z ( 6) -Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -Y ,1/2+X ,1/4+Z ', '( 3) 1/2-X ,1/2-Y ,1/2+Z ( 4) 1/2+Y , -X ,3/4+Z ', '( 5) 1/2-X , Y ,3/4-Z ( 6) -Y , -X , -Z ', '( 7) X ,1/2-Y ,1/4-Z ( 8) 1/2+Y ,1/2+X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y-X, Y , Z ( 5) -Y , -X , Z ( 6) X , X-Y, Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2)+', '', '( 1) X , Y , Z ( 2) -X ,1/2+Y , Z ', '( 3) X ,1/2-Y , Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X ,1/2+Y , -Z ( 5) -Z ,1/2+X ,1/2+Y ( 6) 1/2+Y , -Z ,1/2+X ', '( 7) 1/2-Z , X ,1/2-Y ( 8) 1/2-Y ,1/2-Z , X ( 9) Y ,1/2-Z ,1/2-X ', '(10) 1/2-X , Y ,1/2-Z (11) 1/2-Z ,1/2-X , Y (12) X ,1/2-Y ,1/2-Z ', '(13) 1/2+Y ,1/2+X ,1/2+Z (14) 1/2+Z ,1/2+Y ,1/2+X (15) 1/2+X ,1/2+Z ,1/2+Y ', '(16) Y , X ,1/2-Z (17) 1/2-Z , Y , X (18) X ,1/2-Z , Y ', '(19) -Z ,1/2+Y , -X (20) -X , -Z ,1/2+Y (21) 1/2+X , -Z , -Y ', '(22) -Y ,1/2+X , -Z (23) -Z , -Y ,1/2+X (24) 1/2+Y , -X , -Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3)+', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) X , -Y , -Z ', '( 3) -X , Y , -Z ( 4) -X , -Y , Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/2+X ,1/2+Y , -Z ( 5) -Z ,1/2+X ,1/2+Y ( 6) 1/2+Y , -Z ,1/2+X ', '( 7) 1/2-Z , X ,1/2-Y ( 8) 1/2-Y ,1/2-Z , X ( 9) Y ,1/2-Z ,1/2-X ', '(10) 1/2-X , Y ,1/2-Z (11) 1/2-Z ,1/2-X , Y (12) X ,1/2-Y ,1/2-Z ', '(13) Y , X , Z (14) Z , Y , X (15) X , Z , Y ', '(16) 1/2+Y ,1/2+X , -Z (17) -Z ,1/2+Y ,1/2+X (18) 1/2+X , -Z ,1/2+Y ', '(19) 1/2-Z , Y ,1/2-X (20) 1/2-X ,1/2-Z , Y (21) X ,1/2-Z ,1/2-Y ', '(22) 1/2-Y , X ,1/2-Z (23) 1/2-Z ,1/2-Y , X (24) Y ,1/2-X ,1/2-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y,2/3+Z ( 3) Y-X, -X ,1/3+Z ', '( 4) Y , X , -Z ( 5) -X , Y-X,2/3-Z ( 6) X-Y, -Y ,1/3-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) X-Y, X , Z ( 3) -Y , X-Y, Z ', '( 4) -X , -Y , Z ( 5) Y-X, -X , Z ( 6) Y , Y-X, Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) 1/2+X ,1/2-Y , -Z ', '( 3) -X ,1/2+Y ,1/2-Z ( 4) 1/2-X , -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '\n (0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0)+', '', '( 1) X , Y , Z ( 2) Z , X , Y ( 3) Y , Z , X ', '( 4) 1/4+X ,1/4+Y , -Z ( 5) -Z ,1/4+X ,1/4+Y ( 6) 1/4+Y , -Z ,1/4+X ', '( 7) 1/4-Z ,1/2+X ,3/4-Y ( 8) 3/4-Y ,1/4-Z ,1/2+X ( 9) 1/2+Y ,1/4-Z ,3/4-X ', '(10) 3/4-X ,1/2+Y ,1/4-Z (11) 1/4-Z ,3/4-X ,1/2+Y (12) 1/2+X ,3/4-Y ,1/4-Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) Y , -X , -Z ', '( 3) -X , -Y , Z ( 4) -Y , X , -Z ', '( 5) 1/2-X ,1/2+Y , Z ( 6) 1/2+Y ,1/2+X , -Z ', '( 7) 1/2+X ,1/2-Y , Z ( 8) 1/2-Y ,1/2-X , -Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X-Y, Z ( 3) Y-X, -X , Z ', '( 4) Y , X ,1/2+Z ( 5) -X , Y-X,1/2+Z ( 6) X-Y, -Y ,1/2+Z '] , "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', '\nThe equivalent positions are:', '', '( 1) X , Y , Z ( 2) -Y , X ,1/4+Z ', '( 3) -X , -Y ,1/2+Z ( 4) Y , -X ,3/4+Z ', '( 5) -X , Y , -Z ( 6) -Y , -X ,1/4-Z ', '( 7) X , -Y ,1/2-Z ( 8) Y , X ,3/4-Z '] , }