S4s = [Symmetry.Symel("E", [1 0 0; 0 1 0; 0 0 1])
    Symmetry.Symel("C_2^1", [-1.0 0.0 0.0; 0.0 -1.0 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("S_4^1", [0.0 -1.0 0.0; 1.0 0.0 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_4^3", [0.0 1.0 0.0; -1.0 0.0 -0.0; 0.0 0.0 -1.0])]

S6s = [Symmetry.Symel("E", [1 0 0; 0 1 0; 0 0 1])
    Symmetry.Symel("i", [-1.0 0.0 0.0; 0.0 -1.0 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("C_3^1", [-0.4999999999999998 -0.8660254037844387 0.0; 0.8660254037844387 -0.4999999999999998 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_3^2", [-0.5000000000000003 0.8660254037844384 0.0; -0.8660254037844384 -0.5000000000000003 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("S_6^1", [0.5000000000000001 -0.8660254037844386 0.0; 0.8660254037844386 0.5000000000000001 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_6^5", [0.49999999999999944 0.8660254037844392 0.0; -0.8660254037844392 0.49999999999999944 0.0; 0.0 0.0 -1.0])]

S8s = [Symmetry.Symel("E", [1 0 0; 0 1 0; 0 0 1])
    Symmetry.Symel("C_4^1", [0.0 -1.0 0.0; 1.0 0.0 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_2^1", [-1.0 0.0 0.0; 0.0 -1.0 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_4^3", [0.0 1.0 0.0; -1.0 0.0 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("S_8^1", [0.7071067811865476 -0.7071067811865475 0.0; 0.7071067811865475 0.7071067811865476 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_8^3", [-0.7071067811865474 -0.7071067811865477 -0.0; 0.7071067811865477 -0.7071067811865474 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_8^5", [-0.7071067811865479 0.7071067811865471 0.0; -0.7071067811865471 -0.7071067811865479 -0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_8^7", [0.707106781186547 0.707106781186548 0.0; -0.707106781186548 0.707106781186547 0.0; 0.0 0.0 -1.0])]

S10s = [Symmetry.Symel("E", [1 0 0; 0 1 0; 0 0 1])
    Symmetry.Symel("i", [-1.0 0.0 0.0; 0.0 -1.0 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("C_5^1", [0.30901699437494745 -0.9510565162951535 0.0; 0.9510565162951535 0.30901699437494745 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_5^2", [-0.8090169943749473 -0.5877852522924731 0.0; 0.5877852522924731 -0.8090169943749473 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_5^3", [-0.8090169943749475 0.587785252292473 0.0; -0.587785252292473 -0.8090169943749475 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_5^4", [0.30901699437494734 0.9510565162951535 0.0; -0.9510565162951535 0.30901699437494734 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("S_10^1", [0.8090169943749475 -0.5877852522924731 0.0; 0.5877852522924731 0.8090169943749475 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_10^3", [-0.3090169943749474 -0.9510565162951536 -0.0; 0.9510565162951536 -0.3090169943749474 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_10^7", [-0.30901699437494756 0.9510565162951538 0.0; -0.9510565162951538 -0.30901699437494756 -0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_10^9", [0.8090169943749477 0.5877852522924735 0.0; -0.5877852522924735 0.8090169943749477 0.0; 0.0 0.0 -1.0])]

"""S12s = [Symmetry.Symel("E", [1 0 0; 0 1 0; 0 0 1])
    Symmetry.Symel("C_6^1", [0.5000000000000001 -0.8660254037844386 0.0; 0.8660254037844386 0.5000000000000001 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_3^1", [-0.4999999999999998 -0.8660254037844388 0.0; 0.8660254037844388 -0.4999999999999998 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_2^1", [-1.0 0.0 0.0; 0.0 -1.0 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_3^2", [-0.5000000000000006 0.8660254037844385 0.0; -0.8660254037844385 -0.5000000000000006 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("C_6^5", [0.49999999999999944 0.8660254037844392 0.0; -0.8660254037844392 0.49999999999999944 0.0; 0.0 0.0 1.0])
    Symmetry.Symel("S_12^1", [0.8660254037844387 -0.49999999999999994 0.0; 0.49999999999999994 0.8660254037844387 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_4^1", [0.0 -1.0 0.0; 1.0 0.0 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_12^5", [-0.8660254037844385 -0.5000000000000006 -0.0; 0.5000000000000006 -0.8660254037844385 0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_12^7", [-0.866025403784439 0.49999999999999944 0.0; -0.49999999999999944 -0.866025403784439 -0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_4^3", [0.0 1.0 0.0; -1.0 0.0 -0.0; 0.0 0.0 -1.0])
    Symmetry.Symel("S_12^11", [0.8660254037844383 0.500000000000001 0.0; -0.500000000000001 0.8660254037844383 0.0; 0.0 0.0 -1.0])]
"""
S4cn = ["A", "B", "E"]
S4ct = C4ct
S6cn = ["Ag", "Eg", "Au", "Eu"]
S6ct = C3hct
S8cn = ["A", "B", "E1", "E2", "E3"]
S8ct = [1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0;
        1.0 -1.0  1.0 -1.0  1.0 -1.0  1.0 -1.0;
        2.0  rt2  0.0 -rt2 -2.0 -rt2  0.0  rt2;
        2.0  0.0 -2.0  0.0  2.0  0.0 -2.0  0.0;
        2.0 -rt2  0.0  rt2 -2.0  rt2  0.0 -rt2]
S10cn = ["Ag", "E1g", "E2g", "Au", "E1u", "E2u"]
S10ct = C5hct
