const mat3 orientations[24] = 
{
{{1.000000, 0.000000, 0.000000}, {0.000000, 1.000000, 0.000000}, {0.000000, 0.000000, 1.000000}},
{{0.000000, 1.000000, 0.000000}, {-1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, 1.000000}},
{{-1.000000, 0.000000, 0.000000}, {0.000000, -1.000000, 0.000000}, {0.000000, 0.000000, 1.000000}},
{{0.000000, -1.000000, 0.000000}, {1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, 1.000000}},
{{0.000000, 0.000000, -1.000000}, {0.000000, 1.000000, 0.000000}, {1.000000, 0.000000, 0.000000}},
{{0.000000, 1.000000, 0.000000}, {0.000000, 0.000000, 1.000000}, {1.000000, 0.000000, 0.000000}},
{{0.000000, 0.000000, 1.000000}, {0.000000, -1.000000, 0.000000}, {1.000000, 0.000000, 0.000000}},
{{0.000000, -1.000000, 0.000000}, {0.000000, 0.000000, -1.000000}, {1.000000, 0.000000, 0.000000}},
{{-1.000000, 0.000000, 0.000000}, {0.000000, 1.000000, 0.000000}, {0.000000, 0.000000, -1.000000}},
{{0.000000, 1.000000, 0.000000}, {1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, -1.000000}},
{{1.000000, 0.000000, 0.000000}, {0.000000, -1.000000, 0.000000}, {0.000000, 0.000000, -1.000000}},
{{0.000000, -1.000000, 0.000000}, {-1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, -1.000000}},
{{0.000000, 0.000000, 1.000000}, {0.000000, 1.000000, 0.000000}, {-1.000000, 0.000000, 0.000000}},
{{0.000000, 1.000000, 0.000000}, {0.000000, 0.000000, -1.000000}, {-1.000000, 0.000000, 0.000000}},
{{0.000000, 0.000000, -1.000000}, {0.000000, -1.000000, 0.000000}, {-1.000000, 0.000000, 0.000000}},
{{0.000000, -1.000000, 0.000000}, {0.000000, 0.000000, 1.000000}, {-1.000000, 0.000000, 0.000000}},
{{1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, 1.000000}, {0.000000, -1.000000, 0.000000}},
{{0.000000, 0.000000, 1.000000}, {-1.000000, 0.000000, 0.000000}, {0.000000, -1.000000, 0.000000}},
{{-1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, -1.000000}, {0.000000, -1.000000, 0.000000}},
{{0.000000, 0.000000, -1.000000}, {1.000000, 0.000000, 0.000000}, {0.000000, -1.000000, 0.000000}},
{{1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, -1.000000}, {0.000000, 1.000000, 0.000000}},
{{0.000000, 0.000000, -1.000000}, {-1.000000, 0.000000, 0.000000}, {0.000000, 1.000000, 0.000000}},
{{-1.000000, 0.000000, 0.000000}, {0.000000, 0.000000, 1.000000}, {0.000000, 1.000000, 0.000000}},
{{0.000000, 0.000000, 1.000000}, {1.000000, 0.000000, 0.000000}, {0.000000, 1.000000, 0.000000}},
};