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import math
def rotation_z(theta):
"""Generates a rotation matrix about the z-axis."""
return [math.cos(theta), -math.sin(theta), 0,
math.sin(theta), math.cos(theta), 0,
0, 0, 1]
def rotation_x(theta):
"""Generates a rotation matrix about the x-axis."""
return [1, 0, 0,
0, math.cos(theta), -math.sin(theta),
0, math.sin(theta), math.cos(theta)]
def rotation_y(theta):
"""Generates a rotation matrix about the y-axis."""
return [math.cos(theta), 0, math.sin(theta),
0, 1, 0,
-math.sin(theta), 0, math.cos(theta)]
def rotation_c2_xy(theta):
"""Generates a C2 rotation matrix in the xy-plane."""
return [math.cos(2 * theta), math.sin(2 * theta), 0,
math.sin(2 * theta), -math.cos(2 * theta), 0,
0, 0, -1]
def rotation_c3_111():
"""Generates a C3 rotation matrix along the (1,1,1) axis."""
return [0, 0, 1, 1, 0, 0, 0, 1, 0]
def rotation_c3_minus1_minus1_1():
"""Generates a C3 rotation matrix along the (-1,-1,1) axis."""
return [0, 1, 0, 0, 0, 1, 1, 0, 0]
def rotation_c3_1_minus1_minus1():
"""Generates a C3 rotation matrix along the (1,-1,-1) axis."""
return [0, 1, 0, 1, 0, 0, 0, 0, 1]
def rotation_c3_minus1_1_minus1():
"""Generates a C3 rotation matrix along the (-1,1,-1) axis."""
return [0, 0, 1, 0, 1, 0, 1, 0, 0]
def rotation_c3_minus1_1_1():
"""Generates a C3 rotation matrix along the (-1,1,-1) axis."""
return [0, -1, 0, 0, 0, 1, -1, 0, 0]
def rotation_c3_1_minus1_1():
"""Generates a C3 rotation matrix along the (-1,1,-1) axis."""
return [0, -1, 0, 0, 0, -1, 1, 0, 0]
def rotation_c3_minus1_minus1_minus1():
"""Generates a C3 rotation matrix along the (-1,-1,-1) axis."""
return [0, 1, 0, 0, 0, 1, 1, 0, 0]
def multiply_matrices(matrix1, matrix2):
"""Multiplies two 3x3 matrices represented as lists."""
result = []
for i in range(3): # Iterate through rows of the result
for j in range(3): # Iterate through columns of the result
element = 0
for k in range(3): # Iterate through elements for dot product
element += matrix1[i * 3 + k] * matrix2[k * 3 + j]
result.append(element)
return result
def rotation_c3_1_1_minus1():
"""Generates a C3 rotation matrix along the (11-1) axis."""
return [1, 0, 0, 0, 1, 0, 0, 0, 1]
def rotation_c2_icosahedral(phi):
"""
Generates a C2 rotation matrix for the icosahedral group.
Args:
phi: The angle around the z-axis to rotate the C2 axis.
Returns:
A 3x3 rotation matrix as a flattened list.
"""
c_phi = math.cos(phi)
s_phi = math.sin(phi)
# Rotation matrix for C2 about an axis in the xy plane.
# The axis is rotated by phi around the z-axis.
rotation_matrix = [
c_phi * c_phi - s_phi * s_phi, 2 * c_phi * s_phi, 0,
2 * c_phi * s_phi, s_phi * s_phi - c_phi * c_phi, 0,
0, 0, -1
]
return rotation_matrix
def rotation_c3_icosahedral(phi, theta):
"""
Generates a C3 rotation matrix for the icosahedral group.
Args:
phi: The azimuthal angle (around the z-axis).
theta: The polar angle (from the z-axis).
Returns:
A 3x3 rotation matrix as a flattened list.
"""
c_phi = math.cos(phi)
s_phi = math.sin(phi)
c_theta = math.cos(theta)
s_theta = math.sin(theta)
# Rotation matrix for a C3 rotation about an axis defined by (theta, phi)
# The axis is defined in spherical coordinates.
a = 1/math.sqrt(3)
u_x = s_theta * c_phi;
u_y = s_theta * s_phi;
u_z = c_theta;
rotation_matrix = [
c_phi*c_phi*(1-a)+a, c_phi*s_phi*(1-a) - u_z*a*math.sqrt(3), c_phi*c_theta*(1-a) + u_y*a*math.sqrt(3),
s_phi*c_phi*(1-a) + u_z*a*math.sqrt(3), s_phi*s_phi*(1-a)+a, s_phi*c_theta*(1-a) - u_x*a*math.sqrt(3),
c_theta*c_phi*(1-a) - u_y*a*math.sqrt(3), c_theta*s_phi*(1-a) + u_x*a*math.sqrt(3), c_theta*c_theta*(1-a)+a,
]
return rotation_matrix
def rotation_c5_icosahedral(phi, theta):
"""
Generates a C5 rotation matrix for the icosahedral group.
Args:
phi: The azimuthal angle (around the z-axis).
theta: The polar angle (from the z-axis).
Returns:
A 3x3 rotation matrix as a flattened list.
"""
c_phi = math.cos(phi)
s_phi = math.sin(phi)
c_theta = math.cos(theta)
s_theta = math.sin(theta)
# Rotation matrix for a C5 rotation about an axis defined by (theta, phi)
# The axis is defined in spherical coordinates.
angle = 2 * math.pi / 5 # 72 degrees
u_x = s_theta * c_phi
u_y = s_theta * s_phi
u_z = c_theta
c = math.cos(angle)
s = math.sin(angle)
one_minus_c = 1 - c
rotation_matrix = [
u_x * u_x * one_minus_c + c, u_x * u_y * one_minus_c - u_z * s, u_x * u_z * one_minus_c + u_y * s,
u_y * u_x * one_minus_c + u_z * s, u_y * u_y * one_minus_c + c, u_y * u_z * one_minus_c - u_x * s,
u_z * u_x * one_minus_c - u_y * s, u_z * u_y * one_minus_c + u_x * s, u_z * u_z * one_minus_c + c,
]
return rotation_matrix
def generate_point_group_matrices(point_group_symbol):
"""Generates rotation matrices for a given point group."""
def flatten(m33):
return [item for sublist in m33 for item in sublist]
def zeroify(m0):
m1 = [ 0 if math.fabs(x) < 0.00000001 else x for x in m0]
m2 = [ 0.5 if math.fabs(x-0.5) < 0.00000001 else x for x in m1]
m3 = [-0.5 if math.fabs(x+0.5) < 0.00000001 else x for x in m2]
return m3
matrices = {"E": [1, 0, 0, 0, 1, 0, 0, 0, 1]} # Identity
point_groups = {
"C2": {
"C2(z)": rotation_z(math.pi),
},
"C3": {
"C3(z)": rotation_z(2 * math.pi / 3),
"C3(z)^2": rotation_z(4 * math.pi / 3),
},
"C4": {
"C4(z)": rotation_z(math.pi / 2),
"C4(z)^2": rotation_z(math.pi),
"C4(z)^3": rotation_z(3 * math.pi / 2),
},
"C5": {
"C5(z)": rotation_z(2 * math.pi / 5),
"C5(z)^2": rotation_z(4 * math.pi / 5),
"C5(z)^3": rotation_z(6 * math.pi / 5),
"C5(z)^4": rotation_z(8 * math.pi / 5),
},
"C6": {
"C6(z)": rotation_z(math.pi / 3),
"C6(z)^2": rotation_z(2 * math.pi / 3),
"C6(z)^3": rotation_z(math.pi),
"C6(z)^4": rotation_z(4 * math.pi / 3),
"C6(z)^5": rotation_z(5 * math.pi / 3),
},
"D2": {
"C2(z)": rotation_z(math.pi),
"C2(x)": [1, 0, 0, 0, -1, 0, 0, 0, -1],
"C2(y)": [-1, 0, 0, 0, 1, 0, 0, 0, -1],
},
"D3": {
"C3(z)": rotation_z(2 * math.pi / 3),
"C3(z)^2": rotation_z(4 * math.pi / 3),
"C2(1)": rotation_c2_xy(0),
"C2(2)": rotation_c2_xy(math.pi / 3),
"C2(3)": rotation_c2_xy(-math.pi / 3),
},
"D4": {
"C4(z)": rotation_z(math.pi / 2),
"C4(z)^2": rotation_z(math.pi),
"C4(z)^3": rotation_z(3 * math.pi / 2),
"C2(1)": rotation_c2_xy(0),
"C2(2)": rotation_c2_xy(math.pi / 4),
"C2(3)": rotation_c2_xy(3 * math.pi / 4),
"C2(4)": rotation_c2_xy(5 * math.pi / 4),
},
"D5": {
"C5(z)": rotation_z(2 * math.pi / 5),
"C5(z)^2": rotation_z(4 * math.pi / 5),
"C5(z)^3": rotation_z(6 * math.pi / 5),
"C5(z)^4": rotation_z(8 * math.pi / 5),
"C2(1)": rotation_c2_xy(0),
"C2(2)": rotation_c2_xy(math.pi / 5),
"C2(3)": rotation_c2_xy(3 * math.pi / 5),
"C2(4)": rotation_c2_xy(5 * math.pi / 5),
"C2(5)": rotation_c2_xy(7 * math.pi / 5),
},
"D6": {
"C6(z)": rotation_z(math.pi / 3),
"C6(z)^2": rotation_z(2 * math.pi / 3),
"C6(z)^3": rotation_z(math.pi),
"C6(z)^4": rotation_z(4 * math.pi / 3),
"C6(z)^5": rotation_z(5 * math.pi / 3),
"C2(1)": rotation_c2_xy(0),
"C2(2)": rotation_c2_xy(math.pi / 6),
"C2(3)": rotation_c2_xy(3 * math.pi / 6),
"C2(4)": rotation_c2_xy(5 * math.pi / 6),
"C2(5)": rotation_c2_xy(7 * math.pi / 6),
"C2(6)": rotation_c2_xy(9 * math.pi / 6),
},
"T": {
"C2(x)": rotation_x(math.pi),
"C2(y)": rotation_y(math.pi),
"C2(z)": rotation_z(math.pi),
"C3(111)": rotation_c3_111(),
"C3(-1-11)": rotation_c3_minus1_minus1_1(),
"C3(1-1-1)": rotation_c3_1_minus1_minus1(),
"C3(-11-1)": rotation_c3_minus1_1_minus1(),
"C3(11-1)": rotation_c3_1_1_minus1(),
"C3(-1-1-1)": rotation_c3_minus1_minus1_minus1(),
"C3(-111)": rotation_c3_minus1_1_1(),
"C3(1-11)": rotation_c3_1_minus1_1(),
},
"Th": {
"i": [-1, 0, 0, 0, -1, 0, 0, 0, -1],
"S6(111)": multiply_matrices(rotation_c3_111(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-1-11)": multiply_matrices(rotation_c3_minus1_minus1_1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(1-1-1)": multiply_matrices(rotation_c3_1_minus1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-11-1)": multiply_matrices(rotation_c3_minus1_1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(11-1)": multiply_matrices(rotation_c3_1_1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-1-1-1)": multiply_matrices(rotation_c3_minus1_minus1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-111)": multiply_matrices(rotation_c3_minus1_1_1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(1-11)": multiply_matrices(rotation_c3_1_minus1_1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
},
"Td": {
"C2(x)": rotation_x(math.pi),
"C2(y)": rotation_y(math.pi),
"C2(z)": rotation_z(math.pi),
"C3(111)": rotation_c3_111(),
"C3(-1-11)": rotation_c3_minus1_minus1_1(),
"C3(1-1-1)": rotation_c3_1_minus1_minus1(),
"C3(-11-1)": rotation_c3_minus1_1_minus1(),
"C3(11-1)": rotation_c3_1_1_minus1(),
"C3(-1-1-1)": rotation_c3_minus1_minus1_minus1(),
"C3(-111)": rotation_c3_minus1_1_1(),
"C3(1-11)": rotation_c3_1_minus1_1(),
"S4(x)": multiply_matrices(rotation_x(math.pi/2), flatten([[-1,0,0],[0,1,0],[0,0,1]])),
"S4(y)": multiply_matrices(rotation_y(math.pi/2), flatten([[1,0,0],[0,-1,0],[0,0,1]])),
"S4(z)": multiply_matrices(rotation_z(math.pi/2), flatten([[1,0,0],[0,1,0],[0,0,-1]])),
"S4(x)^-1": multiply_matrices(rotation_x(3*math.pi/2), flatten([[-1,0,0],[0,1,0],[0,0,1]])),
"S4(y)^-1": multiply_matrices(rotation_y(3*math.pi/2), flatten([[1,0,0],[0,-1,0],[0,0,1]])),
"S4(z)^-1": multiply_matrices(rotation_z(3*math.pi/2), flatten([[1,0,0],[0,1,0],[0,0,-1]])),
"sigma_d(xy)": flatten([[0,1,0],[1,0,0],[0,0,1]]),
"sigma_d(xz)": flatten([[0,0,1],[0,1,0],[1,0,0]]),
"sigma_d(yz)": flatten([[1,0,0],[0,0,1],[0,1,0]]),
"sigma_d(x-y)": flatten([[0,-1,0],[-1,0,0],[0,0,1]]),
"sigma_d(x-z)": flatten([[0,0,-1],[0,1,0],[-1,0,0]]),
"sigma_d(y-z)": flatten([[1,0,0],[0,0,-1],[0,-1,0]]),
},
"O": {
"C4(x)": rotation_x(math.pi/2),
"C4(x)^-1": rotation_x(3*math.pi/2),
"C4(y)": rotation_y(math.pi/2),
"C4(y)^-1": rotation_y(3*math.pi/2),
"C4(z)": rotation_z(math.pi/2),
"C4(z)^-1": rotation_z(3*math.pi/2),
"C2(x)": rotation_x(math.pi),
"C2(y)": rotation_y(math.pi),
"C2(z)": rotation_z(math.pi),
"C3(111)": rotation_c3_111(),
"C3(-1-11)": rotation_c3_minus1_minus1_1(),
"C3(1-1-1)": rotation_c3_1_minus1_minus1(),
"C3(-11-1)": rotation_c3_minus1_1_minus1(),
"C3(11-1)": rotation_c3_1_1_minus1(),
"C3(-1-1-1)": rotation_c3_minus1_minus1_minus1(),
"C3(-111)": rotation_c3_minus1_1_1(),
"C3(1-11)": rotation_c3_1_minus1_1(),
"C2(xy)": flatten([[0,1,0],[1,0,0],[0,0,1]]),
"C2(xz)": flatten([[0,0,1],[0,1,0],[1,0,0]]),
"C2(yz)": flatten([[1,0,0],[0,0,1],[0,1,0]]),
"C2(x-y)": flatten([[0,-1,0],[-1,0,0],[0,0,1]]),
"C2(x-z)": flatten([[0,0,-1],[0,1,0],[-1,0,0]]),
"C2(y-z)": flatten([[1,0,0],[0,0,-1],[0,-1,0]]),
},
"Oh": {
"i": [-1, 0, 0, 0, -1, 0, 0, 0, -1],
"C4(x)": rotation_x(math.pi/2),
"C4(x)^-1": rotation_x(3*math.pi/2),
"C4(y)": rotation_y(math.pi/2),
"C4(y)^-1": rotation_y(3*math.pi/2),
"C4(z)": rotation_z(math.pi/2),
"C4(z)^-1": rotation_z(3*math.pi/2),
"C2(x)": rotation_x(math.pi),
"C2(y)": rotation_y(math.pi),
"C2(z)": rotation_z(math.pi),
"C3(111)": rotation_c3_111(),
"C3(-1-11)": rotation_c3_minus1_minus1_1(),
"C3(1-1-1)": rotation_c3_1_minus1_minus1(),
"C3(-11-1)": rotation_c3_minus1_1_minus1(),
"C3(11-1)": rotation_c3_1_1_minus1(),
"C3(-1-1-1)": rotation_c3_minus1_minus1_minus1(),
"C3(-111)": rotation_c3_minus1_1_1(),
"C3(1-11)": rotation_c3_1_minus1_1(),
"C2(xy)": flatten([[0,1,0],[1,0,0],[0,0,1]]),
"C2(xz)": flatten([[0,0,1],[0,1,0],[1,0,0]]),
"C2(yz)": flatten([[1,0,0],[0,0,1],[0,1,0]]),
"C2(x-y)": flatten([[0,-1,0],[-1,0,0],[0,0,1]]),
"C2(x-z)": flatten([[0,0,-1],[0,1,0],[-1,0,0]]),
"C2(y-z)": flatten([[1,0,0],[0,0,-1],[0,-1,0]]),
"sigma_h": flatten([[1,0,0],[0,1,0],[0,0,-1]]),
"sigma_v(x)": flatten([[-1,0,0],[0,1,0],[0,0,1]]),
"sigma_v(y)": flatten([[1,0,0],[0,-1,0],[0,0,1]]),
"sigma_v(z)": flatten([[1,0,0],[0,1,0],[0,0,-1]]),
"sigma_d(xy)": flatten([[0,1,0],[1,0,0],[0,0,1]]),
"sigma_d(xz)": flatten([[0,0,1],[0,1,0],[1,0,0]]),
"sigma_d(yz)": flatten([[1,0,0],[0,0,1],[0,1,0]]),
"sigma_d(x-y)": flatten([[0,-1,0],[-1,0,0],[0,0,1]]),
"sigma_d(x-z)": flatten([[0,0,-1],[0,1,0],[-1,0,0]]),
"sigma_d(y-z)": flatten([[1,0,0],[0,0,-1],[0,-1,0]]),
"S4(x)": multiply_matrices(rotation_x(math.pi/2), flatten([[-1,0,0],[0,1,0],[0,0,1]])),
"S4(y)": multiply_matrices(rotation_y(math.pi/2), flatten([[1,0,0],[0,-1,0],[0,0,1]])),
"S4(z)": multiply_matrices(rotation_z(math.pi/2), flatten([[1,0,0],[0,1,0],[0,0,-1]])),
"S4(x)^-1": multiply_matrices(rotation_x(3*math.pi/2), flatten([[-1,0,0],[0,1,0],[0,0,1]])),
"S4(y)^-1": multiply_matrices(rotation_y(3*math.pi/2), flatten([[1,0,0],[0,-1,0],[0,0,1]])),
"S4(z)^-1": multiply_matrices(rotation_z(3*math.pi/2), flatten([[1,0,0],[0,1,0],[0,0,-1]])),
"S6(111)": multiply_matrices(rotation_c3_111(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-1-11)": multiply_matrices(rotation_c3_minus1_minus1_1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(1-1-1)": multiply_matrices(rotation_c3_1_minus1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-11-1)": multiply_matrices(rotation_c3_minus1_1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(11-1)": multiply_matrices(rotation_c3_1_1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-1-1-1)": multiply_matrices(rotation_c3_minus1_minus1_minus1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(-111)": multiply_matrices(rotation_c3_minus1_1_1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(1-11)": multiply_matrices(rotation_c3_1_minus1_1(), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
},
"I": {
"C2(1)": rotation_c2_icosahedral(0),
"C2(2)": rotation_c2_icosahedral(math.pi/5),
"C2(3)": rotation_c2_icosahedral(2*math.pi/5),
"C2(4)": rotation_c2_icosahedral(3*math.pi/5),
"C2(5)": rotation_c2_icosahedral(4*math.pi/5),
"C2(6)": rotation_c2_icosahedral(math.pi),
"C2(7)": rotation_c2_icosahedral(6*math.pi/5),
"C2(8)": rotation_c2_icosahedral(7*math.pi/5),
"C2(9)": rotation_c2_icosahedral(8*math.pi/5),
"C2(10)": rotation_c2_icosahedral(9*math.pi/5),
"C3(1)": rotation_c3_icosahedral(0, 0),
"C3(2)": rotation_c3_icosahedral(2*math.pi/5, 0),
"C3(3)": rotation_c3_icosahedral(4*math.pi/5, 0),
"C3(4)": rotation_c3_icosahedral(6*math.pi/5, 0),
"C3(5)": rotation_c3_icosahedral(8*math.pi/5, 0),
"C3(6)": rotation_c3_icosahedral(0, math.acos(1/math.sqrt(5))),
"C3(7)": rotation_c3_icosahedral(2*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(8)": rotation_c3_icosahedral(4*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(9)": rotation_c3_icosahedral(6*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(10)": rotation_c3_icosahedral(8*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(11)": rotation_c3_icosahedral(0, -math.acos(1/math.sqrt(5))),
"C3(12)": rotation_c3_icosahedral(2*math.pi/5, -math.acos(1/math.sqrt(5))),
"C3(13)": rotation_c3_icosahedral(4*math.pi/5, -math.acos(1/math.sqrt(5))),
"C3(14)": rotation_c3_icosahedral(6*math.pi/5, -math.acos(1/math.sqrt(5))),
"C3(15)": rotation_c3_icosahedral(8*math.pi/5, -math.acos(1/math.sqrt(5))),
"C5(1)": rotation_c5_icosahedral(0, 0),
"C5(2)": rotation_c5_icosahedral(2*math.pi/5, 0),
"C5(3)": rotation_c5_icosahedral(4*math.pi/5, 0),
"C5(4)": rotation_c5_icosahedral(6*math.pi/5, 0),
"C5(5)": rotation_c5_icosahedral(8*math.pi/5, 0),
"C5(6)": rotation_c5_icosahedral(0, math.acos(math.sqrt(5)/3)),
"C5(7)": rotation_c5_icosahedral(2*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(8)": rotation_c5_icosahedral(4*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(9)": rotation_c5_icosahedral(6*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(10)": rotation_c5_icosahedral(8*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(11)": rotation_c5_icosahedral(0, -math.acos(math.sqrt(5)/3)),
"C5(12)": rotation_c5_icosahedral(2*math.pi/5, -math.acos(math.sqrt(5)/3)),
"C5(13)": rotation_c5_icosahedral(4*math.pi/5, -math.acos(math.sqrt(5)/3)),
"C5(14)": rotation_c5_icosahedral(6*math.pi/5, -math.acos(math.sqrt(5)/3)),
"C5(15)": rotation_c5_icosahedral(8*math.pi/5, -math.acos(math.sqrt(5)/3)),
},
"Ih-broken": {
"i": [-1, 0, 0, 0, -1, 0, 0, 0, -1],
"C2(1)": rotation_c2_icosahedral(0),
"C2(2)": rotation_c2_icosahedral(math.pi/5),
"C2(3)": rotation_c2_icosahedral(2*math.pi/5),
"C2(4)": rotation_c2_icosahedral(3*math.pi/5),
"C2(5)": rotation_c2_icosahedral(4*math.pi/5),
"C2(6)": rotation_c2_icosahedral(math.pi),
"C2(7)": rotation_c2_icosahedral(6*math.pi/5),
"C2(8)": rotation_c2_icosahedral(7*math.pi/5),
"C2(9)": rotation_c2_icosahedral(8*math.pi/5),
"C2(10)": rotation_c2_icosahedral(9*math.pi/5),
"C3(1)": rotation_c3_icosahedral(0, 0),
"C3(2)": rotation_c3_icosahedral(2*math.pi/5, 0),
"C3(3)": rotation_c3_icosahedral(4*math.pi/5, 0),
"C3(4)": rotation_c3_icosahedral(6*math.pi/5, 0),
"C3(5)": rotation_c3_icosahedral(8*math.pi/5, 0),
"C3(6)": rotation_c3_icosahedral(0, math.acos(1/math.sqrt(5))),
"C3(7)": rotation_c3_icosahedral(2*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(8)": rotation_c3_icosahedral(4*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(9)": rotation_c3_icosahedral(6*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(10)": rotation_c3_icosahedral(8*math.pi/5, math.acos(1/math.sqrt(5))),
"C3(11)": rotation_c3_icosahedral(0, -math.acos(1/math.sqrt(5))),
"C3(12)": rotation_c3_icosahedral(2*math.pi/5, -math.acos(1/math.sqrt(5))),
"C3(13)": rotation_c3_icosahedral(4*math.pi/5, -math.acos(1/math.sqrt(5))),
"C3(14)": rotation_c3_icosahedral(6*math.pi/5, -math.acos(1/math.sqrt(5))),
"C3(15)": rotation_c3_icosahedral(8*math.pi/5, -math.acos(1/math.sqrt(5))),
"C5(1)": rotation_c5_icosahedral(0, 0),
"C5(2)": rotation_c5_icosahedral(2*math.pi/5, 0),
"C5(3)": rotation_c5_icosahedral(4*math.pi/5, 0),
"C5(4)": rotation_c5_icosahedral(6*math.pi/5, 0),
"C5(5)": rotation_c5_icosahedral(8*math.pi/5, 0),
"C5(6)": rotation_c5_icosahedral(0, math.acos(math.sqrt(5)/3)),
"C5(7)": rotation_c5_icosahedral(2*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(8)": rotation_c5_icosahedral(4*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(9)": rotation_c5_icosahedral(6*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(10)": rotation_c5_icosahedral(8*math.pi/5, math.acos(math.sqrt(5)/3)),
"C5(11)": rotation_c5_icosahedral(0, -math.acos(math.sqrt(5)/3)),
"C5(12)": rotation_c5_icosahedral(2*math.pi/5, -math.acos(math.sqrt(5)/3)),
"C5(13)": rotation_c5_icosahedral(4*math.pi/5, -math.acos(math.sqrt(5)/3)),
"C5(14)": rotation_c5_icosahedral(6*math.pi/5, -math.acos(math.sqrt(5)/3)),
"C5(15)": rotation_c5_icosahedral(8*math.pi/5, -math.acos(math.sqrt(5)/3)),
"sigma_h(1)": multiply_matrices(rotation_c2_icosahedral(0), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(2)": multiply_matrices(rotation_c2_icosahedral(math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(3)": multiply_matrices(rotation_c2_icosahedral(2*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(4)": multiply_matrices(rotation_c2_icosahedral(3*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(5)": multiply_matrices(rotation_c2_icosahedral(4*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(6)": multiply_matrices(rotation_c2_icosahedral(math.pi), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(7)": multiply_matrices(rotation_c2_icosahedral(6*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(8)": multiply_matrices(rotation_c2_icosahedral(7*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(9)": multiply_matrices(rotation_c2_icosahedral(8*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"sigma_h(10)": multiply_matrices(rotation_c2_icosahedral(9*math.pi/5), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(1)": multiply_matrices(rotation_c3_icosahedral(0, 0), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(2)": multiply_matrices(rotation_c3_icosahedral(2*math.pi/5, 0), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(3)": multiply_matrices(rotation_c3_icosahedral(4*math.pi/5, 0), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
"S6(4)": multiply_matrices(rotation_c3_icosahedral(6*math.pi/5, 0), [-1, 0, 0, 0, -1, 0, 0, 0, -1]),
},
}
if point_group_symbol in point_groups:
matrices.update(point_groups[point_group_symbol])
zm = {}
for key in matrices:
zm[key] = zeroify(matrices[key])
return zm
else:
return "Point group not supported"
if __name__ == "__main__":
print(generate_point_group_matrices("C2"))
print(generate_point_group_matrices("C3"))
print(generate_point_group_matrices("C4"))
print(generate_point_group_matrices("C5"))
print(generate_point_group_matrices("D2"))
print(generate_point_group_matrices("D3"))
print(generate_point_group_matrices("D4"))
# https://www.rcsb.org/search?request=%7B%22query%22%3A%7B%22type%22%3A%22group%22%2C%22logical_operator%22%3A%22and%22%2C%22nodes%22%3A%5B%7B%22type%22%3A%22group%22%2C%22logical_operator%22%3A%22and%22%2C%22nodes%22%3A%5B%7B%22type%22%3A%22group%22%2C%22nodes%22%3A%5B%7B%22type%22%3A%22terminal%22%2C%22service%22%3A%22text%22%2C%22parameters%22%3A%7B%22attribute%22%3A%22rcsb_struct_symmetry.symbol%22%2C%22operator%22%3A%22exact_match%22%2C%22negation%22%3Afalse%2C%22value%22%3A%22D4%22%7D%7D%5D%2C%22logical_operator%22%3A%22and%22%7D%5D%2C%22label%22%3A%22text%22%7D%5D%7D%2C%22return_type%22%3A%22entry%22%2C%22request_options%22%3A%7B%22paginate%22%3A%7B%22start%22%3A0%2C%22rows%22%3A25%7D%2C%22results_content_type%22%3A%5B%22experimental%22%5D%2C%22sort%22%3A%5B%7B%22sort_by%22%3A%22score%22%2C%22direction%22%3A%22desc%22%7D%5D%2C%22scoring_strategy%22%3A%22combined%22%7D%2C%22request_info%22%3A%7B%22query_id%22%3A%221efe9d9f2c283fc40e6f0d8559eaf48f%22%7D%7D
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