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import numpy as np from scipy.constants import golden as phi def icosahedral(cls): g1 = tetrahedral(cls).as_quat() a = 0.5 b = 0.5 / phi c = phi / 2 g2 = np.array([[+a, +b, +c, 0], [+a, +b, -c, 0], [+a, +c, 0, +b], [+a, +c, 0, -b], [+a, -b, +c, 0], [+a, -b, -c, 0], [+a, -c, 0, +b], [+a, -c, 0, -b], [+a, 0, +b, +c], [+a, 0, +b, -c], [+a, 0, -b, +c], [+a, 0, -b, -c], [+b, +a, 0, +c], [+b, +a, 0, -c], [+b, +c, +a, 0], [+b, +c, -a, 0], [+b, -a, 0, +c], [+b, -a, 0, -c], [+b, -c, +a, 0], [+b, -c, -a, 0], [+b, 0, +c, +a], [+b, 0, +c, -a], [+b, 0, -c, +a], [+b, 0, -c, -a], [+c, +a, +b, 0], [+c, +a, -b, 0], [+c, +b, 0, +a], [+c, +b, 0, -a], [+c, -a, +b, 0], [+c, -a, -b, 0], [+c, -b, 0, +a], [+c, -b, 0, -a], [+c, 0, +a, +b], [+c, 0, +a, -b], [+c, 0, -a, +b], [+c, 0, -a, -b], [0, +a, +c, +b], [0, +a, +c, -b], [0, +a, -c, +b], [0, +a, -c, -b], [0, +b, +a, +c], [0, +b, +a, -c], [0, +b, -a, +c], [0, +b, -a, -c], [0, +c, +b, +a], [0, +c, +b, -a], [0, +c, -b, +a], [0, +c, -b, -a]]) return cls.from_quat(np.concatenate((g1, g2))) def octahedral(cls): g1 = tetrahedral(cls).as_quat() c = np.sqrt(2) / 2 g2 = np.array([[+c, 0, 0, +c], [0, +c, 0, +c], [0, 0, +c, +c], [0, 0, -c, +c], [0, -c, 0, +c], [-c, 0, 0, +c], [0, +c, +c, 0], [0, -c, +c, 0], [+c, 0, +c, 0], [-c, 0, +c, 0], [+c, +c, 0, 0], [-c, +c, 0, 0]]) return cls.from_quat(np.concatenate((g1, g2))) def tetrahedral(cls): g1 = np.eye(4) c = 0.5 g2 = np.array([[c, -c, -c, +c], [c, -c, +c, +c], [c, +c, -c, +c], [c, +c, +c, +c], [c, -c, -c, -c], [c, -c, +c, -c], [c, +c, -c, -c], [c, +c, +c, -c]]) return cls.from_quat(np.concatenate((g1, g2))) def dicyclic(cls, n, axis=2): g1 = cyclic(cls, n, axis).as_rotvec() thetas = np.linspace(0, np.pi, n, endpoint=False) rv = np.pi * np.vstack([np.zeros(n), np.cos(thetas), np.sin(thetas)]).T g2 = np.roll(rv, axis, axis=1) return cls.from_rotvec(np.concatenate((g1, g2))) def cyclic(cls, n, axis=2): thetas = np.linspace(0, 2 * np.pi, n, endpoint=False) rv = np.vstack([thetas, np.zeros(n), np.zeros(n)]).T return cls.from_rotvec(np.roll(rv, axis, axis=1)) def create_group(cls, group, axis='Z'): if not isinstance(group, str): raise ValueError("`group` argument must be a string") permitted_axes = ['x', 'y', 'z', 'X', 'Y', 'Z'] if axis not in permitted_axes: raise ValueError("`axis` must be one of " + ", ".join(permitted_axes)) if group in ['I', 'O', 'T']: symbol = group order = 1 elif group[:1] in ['C', 'D'] and group[1:].isdigit(): symbol = group[:1] order = int(group[1:]) else: raise ValueError("`group` must be one of 'I', 'O', 'T', 'Dn', 'Cn'") if order < 1: raise ValueError("Group order must be positive") axis = 'xyz'.index(axis.lower()) if symbol == 'I': return icosahedral(cls) elif symbol == 'O': return octahedral(cls) elif symbol == 'T': return tetrahedral(cls) elif symbol == 'D': return dicyclic(cls, order, axis=axis) elif symbol == 'C': return cyclic(cls, order, axis=axis) else: assert False
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