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symdata.py
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"""
WYCKOFF DATA
no - Space group number
bl - Bravais lattice
T - Triclinic
'Wyckoff letter' : [Multiplicity, Site symmetry, Wyckoff position]
1 - 2 Triclinic (Tri) -
3 - 15 Monoclinic (Mon) b(c)
16 - 74 Orthorhombic (Orh) a b c
75 - 142 Tetragonal (Tet) c a [110]
143 - 167 Trigonal (Tri) c a [210]
168 - 194 Hexagonal (Hex) c a [210]
195 - 230 Cubic (Cub) a [111] [110]
"""
# importrant!
# check sg_89 ('x', 'x', 0.5) (2 2 2.)
sg = {'sg_1': {'s1': [1, ['1'], ('x', 'y', 'z'), 1]},
'sg_2': {'s1': [1, ['-1'], (0, 0, 0), 1],
's2': [1, ['-1'], (0, 0, 0.5), 0],
's3': [1, ['-1'], (0, 0.5, 0), 0],
's4': [1, ['-1'], (0.5, 0, 0), 0],
's5': [1, ['-1'], (0.5, 0.5, 0), 0],
's6': [1, ['-1'], (0.5, 0, 0.5), 0],
's7': [1, ['-1'], (0, 0.5, 0.5), 0],
's8': [1, ['-1'], (0.5, 0.5, 0.5), 0],
's9': [2, ['1'], ('x', 'y', 'z'), 1]},
'sg_3': {'s1': [1, ['2'], (0, 'y', 0), 1],
's2': [1, ['2'], (0, 'y', 0.5), 0],
's3': [1, ['2'], (0.5, 'y', 0), 0],
's4': [1, ['2'], (0.5, 'y', 0.5), 0],
's5': [2, ['1'], ('x', 'y', 'z'), 1]},
'sg_4': {'s1': [2, ['1'], ('x', 'y', 'z'), 1]},
'sg_5': {'s1': [2, ['2'], (0, 'y', 0), 1],
's2': [2, ['2'], (0, 'y', 0.5), 0],
's3': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_6': {'s1': [1, ['m'], ('x', 0, 'z'), 1],
's2': [1, ['m'], ('x', 0.5, 'z'), 0],
's3': [2, ['1'], ('x', 'y', 'z'), 1]},
'sg_7': {'s1': [2, ['1'], ('x', 'y', 'z'), 1]},
'sg_8': {'s1': [2, ['m'], ('x', 0, 'z'), 1],
's2': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_9': {'s1': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_10': {'s1': [1, ['2/m'], (0, 0, 0), 1],
's2': [1, ['2/m'], (0, 1/2, 0), 0],
's3': [1, ['2/m'], (0, 0, 0.5), 0],
's4': [1, ['2/m'], (0.5, 0, 0), 0],
's5': [1, ['2/m'], (0.5, 0.5, 0), 0],
's6': [1, ['2/m'], (0, 0.5, 0.5), 0],
's7': [1, ['2/m'], (0.5, 0, 0.5), 0],
's8': [1, ['2/m'], (0.5, 0.5, 0.5), 0],
's9': [2, ['2'], (0, 'y', 0), 1],
's10': [2, ['2'], (0.5, 'y', 0), 0],
's11': [2, ['2'], (0, 'y', 0.5), 0],
's12': [2, ['2'], (0.5, 'y', 0.5), 0],
's13': [2, ['m'], ('x', 0, 'z'), 1],
's14': [2, ['m'], ('x', 0.5, 'z'), 0],
's15': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_11': {'s1': [2, ['-1'], (0, 0, 0), 1],
's2': [2, ['-1'], (0.5, 0, 0), 0],
's3': [2, ['-1'], (0, 0, 0.5), 0],
's4': [2, ['-1'], (0.5, 0, 0.5), 0],
's5': [2, ['m'], ('x', 0.25, 'z'), 1],
's6': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_12': {'s1': [2, ['2/m'], (0, 0, 0), 1],
's2': [2, ['2/m'], (0, 0.5, 0), 0],
's3': [2, ['2/m'], (0, 0, 0.5), 0],
's4': [2, ['2/m'], (0, 0.5, 0.5), 0],
's5': [4, ['-1'], (0.25, 0.25, 0), 1],
's6': [4, ['-1'], (0.25, 0.25, 0.5), 0],
's7': [4, ['2'], (0, 'y', 0), 1],
's8': [4, ['2'], (0, 'y', 0.5), 0],
's9': [4, ['m'], ('x', 0, 'z'), 1],
's10': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_13': {'s1': [2, ['-1'], (0, 0, 0), 1],
's2': [2, ['-1'], (0.5, 0.5, 0), 0],
's3': [2, ['-1'], (0, 0.5, 0), 0],
's4': [2, ['-1'], (0.5, 0, 0), 0],
's5': [2, ['2'], (0, 'y', 0.25), 1],
's6': [2, ['2'], (0.5, 'y', 0.25), 0],
's7': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_14': {'s1': [2, ['-1'], (0, 0, 0), 1],
's2': [2, ['-1'], (0.5, 0, 0), 0],
's3': [2, ['-1'], (0, 0, 0.5), 0],
's4': [2, ['-1'], (0.5, 0, 0.5), 0],
's5': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_15': {'s1': [4, ['-1'], (0, 0, 0), 1],
's2': [4, ['-1'], (0, 0.5, 0), 0],
's3': [4, ['-1'], (0.25, 0.25, 0), 0],
's4': [4, ['-1'], (0.25, 0.25, 0.5), 0],
's5': [4, ['2'], (0, 'y', 0.25), 1],
's6': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_16': {'s1': [2, ['x', 'y', '2'], (0.5, 0.5, 'z'), 1],
's2': [2, ['x', 'y', '2'], (0, 0.5, 'z'), 0],
's3': [2, ['x', 'y', '2'], (0.5, 0, 'z'), 0],
's4': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's5': [2, ['x', '2', 'z'], (0.5, 'y', 0.5), 1],
's6': [2, ['x', '2', 'z'], (0.5, 'y', 0), 0],
's7': [2, ['x', '2', 'z'], (0, 'y', 0.5), 0],
's8': [2, ['x', '2', 'z'], (0, 'y', 0), 0],
's9': [2, ['2', 'y', 'z'], ('x', 0.5, 0.5), 1],
's10': [2, ['2', 'y', 'z'], ('x', 0.5, 0), 0],
's11': [2, ['2', 'y', 'z'], ('x', 0, 0.5), 0],
's12': [2, ['2', 'y', 'z'], ('x', 0, 0), 0],
's13': [2, ['2', '2', '2'], (0.5, 0.5, 0.5), 1],
's14': [2, ['2', '2', '2'], (0, 0.5, 0.5), 1],
's15': [2, ['2', '2', '2'], (0.5, 0, 0.5), 1],
's16': [2, ['2', '2', '2'], (0.5, 0.5, 0), 1],
's17': [2, ['2', '2', '2'], (0, 0, 0.5), 1],
's18': [2, ['2', '2', '2'], (0, 0.5, 0), 1],
's19': [2, ['2', '2', '2'], (0.5, 0, 0), 1],
's20': [2, ['2', '2', '2'], (0, 0, 0), 1],
's21': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_17': {'s1': [2, ['x', '2', 'z'], (0.5, 'y', 0.25), 1],
's2': [2, ['x', '2', 'z'], (0, 'y', 0.25), 0],
's3': [2, ['2', 'y', 'z'], ('x', 0.25, 0), 1],
's4': [2, ['2', 'y', 'z'], ('x', 0, 0), 0],
's5': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_18': {'s1': [2, ['x', 'y', '2'], (0, 0.5, 'z'), 1],
's2': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's3': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_19': {'s1': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_20': {'s1': [4, ['x', '2', 'z'], (0, 'y', 0.25), 1],
's2': [4, ['2', 'y', 'z'], ('x', 0, 0), 1],
's3': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_21': {'s1': [4, ['x', 'y', '2'], (0.25, 0.25, 'z'), 1],
's2': [4, ['x', 'y', '2'], (0, 0.5, 'z'), 0],
's3': [4, ['x', 'y', '2'], (0, 0, 'z'), 0],
's4': [4, ['x', '2', 'z'], (0, 'y', 0.5), 1],
's5': [4, ['x', '2', 'z'], (0, 'y', 0), 0],
's6': [4, ['2', 'y', 'z'], ('x', 0, 0.5), 1],
's7': [4, ['2', 'y', 'z'], ('x', 0, 0), 0],
's8': [2, ['2', '2', '2'], (0, 0, 0.5), 1],
's9': [2, ['2', '2', '2'], (0.5, 0, 0.5), 0],
's10': [2, ['2', '2', '2'], (0, 0.5, 0), 0],
's11': [2, ['2', '2', '2'], (0, 0, 0), 0],
's12': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_22': {'s1': [8, ['2', 'y', 'z'], ('x', 0.25, 0.25), 1],
's2': [8, ['x', '2', 'z'], (0.25, 'y', 0.25), 1],
's3': [8, ['x', 'y', '2'], (0.25, 0.25, 'z'), 1],
's4': [8, ['x', 'y', '2'], (0, 0, 'z'), 0],
's5': [8, ['x', '2', 'z'], (0, 'y', 0), 0],
's6': [8, ['2', 'y', 'z'], ('x', 0, 0), 0],
's7': [4, ['2', '2', '2'], (0.25, 0.25, 0.75), 1],
's8': [4, ['2', '2', '2'], (0.25, 0.25, 0.25), 0],
's9': [4, ['2', '2', '2'], (0, 0, 0.5), 0],
's10': [4, ['2', '2', '2'], (0, 0, 0), 0],
's11': [16, ['1'], ('x', 'y', 'z'), 1]},
'sg_23': {'s1': [4, ['x', 'y', '2'], (0, 0.5, 'z'), 1],
's2': [4, ['x', 'y', '2'], (0, 0, 'z'), 0],
's3': [4, ['x', '2', 'z'], (0.5, 'y', 0), 1],
's4': [4, ['x', '2', 'z'], (0, 'y', 0), 0],
's5': [4, ['2', 'y', 'z'], ('x', 0, 0.5), 1],
's6': [4, ['2', 'y', 'z'], ('x', 0, 0), 0],
's7': [2, ['2', '2', '2'], (0, 0.5, 0), 1],
's8': [2, ['2', '2', '2'], (0, 0, 0.5), 0],
's9': [2, ['2', '2', '2'], (0.5, 0, 0), 0],
's10': [2, ['2', '2', '2'], (0, 0, 0), 0],
's11': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_24': {'s1': [4, ['x', 'y', '2'], (0, 0.25, 'z'), 1],
's2': [4, ['x', '2', 'z'], (0.25, 'y', 0), 1],
's3': [4, ['2', 'y', 'z'], ('x', 0, 0.25), 1],
's4': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_25': {'s1': [2, ['m', 'y', 'z'], (0.5, 'y', 'z'), 1],
's2': [2, ['m', 'y', 'z'], (0, 'y', 'z'), 0],
's3': [2, ['x', 'm', 'z'], ('x', 0.5, 'z'), 1],
's4': [2, ['x', 'm', 'z'], ('x', 0, 'z'), 0],
's5': [1, ['m', 'm', '2'], (0.5, 0.5, 'z'), 1],
's6': [1, ['m', 'm', '2'], (0.5, 0, 'z'), 0],
's7': [1, ['m', 'm', '2'], (0, 0.5, 'z'), 0],
's8': [1, ['m', 'm', '2'], (0, 0, 'z'), 0],
's9': [8, ['1'], ('x', 'y', 'z'), 1]},
'sg_26': {'s1': [2, ['m', 'y', 'z'], (0.5, 'y', 'z'), 1],
's2': [2, ['m', 'y', 'z'], (0, 'y', 'z'), 0],
's3': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_27': {'s1': [2, ['x', 'y', '2'], (0.5, 0.5, 'z'), 1],
's2': [2, ['x', 'y', '2'], (0.5, 0, 'z'), 0],
's3': [2, ['x', 'y', '2'], (0, 0.5, 'z'), 0],
's4': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's5': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_28': {'s1': [2, ['m', 'y', 'z'], (0.25, 'y', 'z'), 1],
's2': [2, ['x', 'y', '2'], (0, 0.5, 'z'), 1],
's3': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's4': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_29': {'s1': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_30': {'s1': [2, ['x', 'y', '2'], (0.5, 0, 'z'), 1],
's2': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's3': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_31': {'s1': [2, ['m', 'y', 'z'], (0, 'y', 'z'), 1],
's2': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_32': {'s1': [2, ['x', 'y', '2'], (0, 0.5, 'z'), 1],
's2': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's3': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_33': {'s1': [4, ['1'], ('x', 'y', 'z'), 1]},
'sg_34': {'s1': [2, ['x', 'y', '2'], (0, 0.5, 'z'), 1],
's2': [2, ['x', 'y', '2'], (0, 0, 'z'), 0],
's3': [4, ['1'], ('x', 'y', 'z'), 1]},
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'sg_172':{'s1':[3, ['2', 'y', 'z'], (0.5, 0.5, 'z')],
's2':[3, ['2', 'y', 'z'], (0, 0, 'z')],
's3':[6, ['1'], ('x', 'y', 'z')]},
'sg_173':{'s1':[2, ['3', 'y', 'z'], (0.333, 0.667, 'z')],
's2':[2, ['3', 'y', 'z'], (0, 0, 'z')],
's3':[6, ['1'], ('x', 'y', 'z')]},
'sg_174':{'s1':[3, ['m', 'y', 'z'], ('x', 'y', 0.5)],
's2':[3, ['m', 'y', 'z'], ('x', 'y', 0)],
's3':[2, ['3', 'y', 'z'], (0.667, 0.333, 'z')],
's4':[2, ['3', 'y', 'z'], (0.333, 0.667, 'z')],
's5':[2, ['3', 'y', 'z'], (0, 0, 'z')],
's6':[1, ['-6', 'y', 'z'], (0.667, 0.333, 0.5)],
's7':[1, ['-6', 'y', 'z'], (0.667, 0.333, 0)],
's8':[1, ['-6', 'y', 'z'], (0.333, 0.667, 0.5)],
's9':[1, ['-6', 'y', 'z'], (0.333, 0.667, 0)],
's10':[1, ['-6', 'y', 'z'], (0, 0, 0.5)],
's11':[1, ['-6', 'y', 'z'], (0, 0, 0)],
's12':[6, ['1'], ('x', 'y', 'z')]},
'sg_176':{'s1':[6, ['m', 'y', 'z'], ('x', 'y', 0.25)],
's2':[6, ['-1'], (0.5, 0, 0)],
's3':[4, ['3', 'y', 'z'], (0.333, 0.667, 'z')],
's4':[4, ['3', 'y', 'z'], (0, 0, 'z')],
's5':[2, ['-6', 'y', 'z'], (0.667, 0.333, 0.25)],
's6':[2, ['-6', 'y', 'z'], (0.333, 0.667, 0.25)],
's7':[2, ['-3', 'y', 'z'], (0, 0, 0)],
's8':[2, ['-3', 'y', 'z'], (0, 0, 0.25)],
's9':[12, ['1'], ('x', 'y', 'z')]},
'sg_182':{'s1':[6, ['x', 'y', '2'], ('x', '2x', 0.25)],
's2':[6, ['x', '2', 'z'], ('x', 0, 0.25)],
's3':[4, ['3', 'y', 'z'], (0.333, 0.667, 'z')],
's4':[4, ['3', 'y', 'z'], (0, 0, 'z')],
's5':[2, ['3', 'y', '2'], (0.333, 0.667, 0.75)],
's6':[2, ['3', 'y', '2'], (0.333, 0.667, 0.25)],
's7':[2, ['3', '2', 'z'], (0, 0, 0)],
's8':[12, ['1'], ('x', 'y', 'z')]},
'sg_183':{'s1':[6, ['x', 'm', 'z'], ('x', '-x', 'z')],
's2':[6, ['x', 'y', 'm'], ('x', 0, 'z')],
's3':[3, ['2', 'm', 'm'], (0.5, 0, 'z')],
's4':[2, ['3', 'm', 'z'], (0.333, 0.667, 'z')],
's5':[1, ['6', 'm', 'm'], (0, 0, 'z')],
's6':[12, ['1'], ('x', 'y', 'z')]},
'sg_186':{'s1':[6, ['x', 'm', 'z'], ('x', '-x', 'z')],
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's3':[2, ['3', 'm', 'z'], (0, 0, 'z')],
's4':[12, ['1'], ('x', 'y', 'z')]},
'sg_187':{'s1':[6, ['x', 'm', 'z'], ('x', '-x', 'z')],
's2':[6, ['m', 'y', 'z'], ('x', 'y', 0.5)],
's3':[6, ['m', 'y', 'z'], ('x', 'y', 0)],
's4':[3, ['m', 'm', '2'], ('x', '-x', 0.5)],
's5':[3, ['m', 'm', '2'], ('x', '-x', 0)],
's6':[2, ['3', 'm', 'z'], (0.667, 0.333, 'z')],
's7':[2, ['3', 'm', 'z'], (0.333, 0.667, 'z')],
's8':[2, ['3', 'm', 'z'], (0, 0, 'z')],
's9':[1, ['-6', 'm', '2'], (0.667, 0.333, 0.5)],
's10':[1, ['-6', 'm', '2'], (0.667, 0.333, 0)],
's11':[1, ['-6', 'm', '2'], (0.333, 0.667, 0.5)],
's12':[1, ['-6', 'm', '2'], (0.333, 0.667, 0)],
's13':[1, ['-6', 'm', '2'], (0, 0, 0.5)],
's14':[1, ['-6', 'm', '2'], (0, 0, 0)],
's15':[12, ['1'], ('x', 'y', 'z')]},
'sg_190':{'s1':[6, ['m', 'y', 'z'], ('x', 'y', 0.25)],
's2':[6, ['x', '2', 'z'], ('x', 0, 0.25)],
's3':[4, ['3', 'y', 'z'], (0.333, 0.667, 'z')],
's4':[4, ['3', 'y', 'z'], (0, 0, 'z')],
's5':[2, ['-6', 'y', 'z'], (0.667, 0.333, 0.25)],
's6':[2, ['-6', 'y', 'z'], (0.333, 0.667, 0.25)],
's7':[2, ['-6', 'y', 'z'], (0, 0, 0.25)],
's8':[2, ['-6', 'y', 'z'], (0, 0, 0)],
's9':[12, ['1'], ('x', 'y', 'z')]},
'sg_194':{'s1':[12, ['x', 'm', 'z'], ('x', '2x', 'z')],
's2':[12, ['m', 'y', 'z'], ('x', 'y', 0.25)],
's3':[12, ['x', '2', 'z'], ('x', 0, 0)],
's4':[6, ['m', 'm', '2'], ('x', '2x', 0.25)],
's5':[6, ['x', '2/m', 'z'], (0.5, 0, 0)],
's6':[4, ['3', 'm', 'z'], (0.333, 0.667, 'z')],
's7':[4, ['3', 'm', 'z'], (0, 0, 'z')],
's8':[2, ['-6', 'm', '2'], (0.333, 0.667, 0.75)],
's9':[2, ['-6', 'm', '2'], (0.333, 0.667, 0.25)],
's10':[2, ['-6', 'm', '2'], (0, 0, 0.25)],
's11':[2, ['-6', 'm', '2'], (0, 0, 0)],
's12':[24, ['1'], ('x', 'y', 'z')]}
}