refMatrices = [
            [[1., 0., 0., 0.],  # 1
             [0., 1., 0., 0.],
             [0., 0., 1., 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, -0.5, 0.30901699, 0.],  # 2
             [-0.5, 0.30901699, -0.80901699, 0.],
             [0.30901699, -0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[0., 1., 0., 0.],  # 3
             [0., 0., -1., 0.],
             [-1., 0., 0., 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, -0.5, -0.30901699, 0.],  # 4
             [-0.5, -0.30901699, -0.80901699, 0.],
             [0.30901699, 0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.5, 0.30901699, -0.80901699, 0.],  # 5
             [-0.30901699, -0.80901699, -0.5, 0.],
             [-0.80901699, 0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, -0.80901699, -0.5, 0.],  # 6
             [-0.80901699, 0.5, -0.30901699, 0.],
             [0.5, 0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, 0.5, -0.30901699, 0.],  # 7
             [0.5, 0.30901699, -0.80901699, 0.],
             [-0.30901699, -0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, -0.5, -0.30901699, 0.],  # 8
             [0.5, -0.30901699, -0.80901699, 0.],
             [0.30901699, -0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, 0.80901699, -0.5, 0.],  # 9
             [-0.80901699, -0.5, -0.30901699, 0.],
             [-0.5, 0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[0.5, -0.30901699, -0.80901699, 0.],  # 10
             [-0.30901699, 0.80901699, -0.5, 0.],
             [0.80901699, 0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0., 0., -1., 0.],  # 11
             [-1., 0., 0., 0.],
             [0., 1., 0., 0.],
             [0., 0., 0., 1.]],

            [[-0.5, -0.30901699, -0.80901699, 0.],  # 12
             [0.30901699, 0.80901699, -0.5, 0.],
             [0.80901699, -0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.5, 0.30901699, -0.80901699, 0.],  # 13
             [0.30901699, -0.80901699, -0.5, 0.],
             [-0.80901699, -0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, -0.80901699, -0.5, 0.],  # 14
             [0.80901699, -0.5, 0.30901699, 0.],
             [-0.5, -0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, 0.5, -0.30901699, 0.],  # 15
             [-0.5, -0.30901699, 0.80901699, 0.],
             [0.30901699, 0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.5, 0.30901699, -0.80901699, 0.],  # 16
             [0.30901699, 0.80901699, 0.5, 0.],
             [0.80901699, -0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.5, 0.30901699, -0.80901699, 0.],  # 17
             [-0.30901699, 0.80901699, 0.5, 0.],
             [0.80901699, 0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0., 0., -1., 0.],
             [1., 0., 0., 0.],
             [0., -1., 0., 0.],
             [0., 0., 0., 1.]],

            [[-0.5, -0.30901699, -0.80901699, 0.],
             [-0.30901699, -0.80901699, 0.5, 0.],
             [-0.80901699, 0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0., -1., 0., 0.],
             [0., 0., 1., 0.],
             [-1., 0., 0., 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, 0.5, 0.30901699, 0.],
             [0.5, 0.30901699, 0.80901699, 0.],
             [0.30901699, 0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, 0.5, -0.30901699, 0.],
             [0.5, -0.30901699, 0.80901699, 0.],
             [0.30901699, -0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, 0.80901699, -0.5, 0.],
             [0.80901699, 0.5, 0.30901699, 0.],
             [0.5, -0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[0.5, -0.30901699, -0.80901699, 0.],
             [0.30901699, -0.80901699, 0.5, 0.],
             [-0.80901699, -0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, -0.5, -0.30901699, 0.],
             [-0.5, 0.30901699, 0.80901699, 0.],
             [-0.30901699, 0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, -0.80901699, 0.5, 0.],
             [-0.80901699, 0.5, 0.30901699, 0.],
             [-0.5, -0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, 0.80901699, 0.5, 0.],
             [0.80901699, 0.5, -0.30901699, 0.],
             [-0.5, 0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[1., 0., 0., 0.],
             [0., -1., 0., 0.],
             [0., 0., -1., 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, 0.80901699, -0.5, 0.],
             [0.80901699, -0.5, -0.30901699, 0.],
             [-0.5, -0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, -0.80901699, -0.5, 0.],
             [-0.80901699, -0.5, 0.30901699, 0.],
             [-0.5, 0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-1., 0., 0., 0.],
             [0., 1., 0., 0.],
             [0., 0., -1., 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, 0.5, -0.30901699, 0.],
             [-0.5, 0.30901699, -0.80901699, 0.],
             [-0.30901699, 0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[0., -1., 0., 0.],
             [0., 0., -1., 0.],
             [1., 0., 0., 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, 0.5, 0.30901699, 0.],
             [-0.5, -0.30901699, -0.80901699, 0.],
             [-0.30901699, -0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.5, -0.30901699, 0.80901699, 0.],
             [-0.30901699, -0.80901699, -0.5, 0.],
             [0.80901699, -0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, 0.80901699, 0.5, 0.],
             [-0.80901699, 0.5, -0.30901699, 0.],
             [-0.5, -0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, -0.5, 0.30901699, 0.],
             [0.5, 0.30901699, -0.80901699, 0.],
             [0.30901699, 0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, 0.5, 0.30901699, 0.],
             [0.5, -0.30901699, -0.80901699, 0.],
             [-0.30901699, 0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, -0.80901699, 0.5, 0.],
             [-0.80901699, -0.5, -0.30901699, 0.],
             [0.5, -0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.5, 0.30901699, 0.80901699, 0.],
             [-0.30901699, 0.80901699, -0.5, 0.],
             [-0.80901699, -0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0., 0., 1., 0.],
             [-1., 0., 0., 0.],
             [0., -1., 0., 0.],
             [0., 0., 0., 1.]],

            [[0.5, 0.30901699, 0.80901699, 0.],
             [0.30901699, 0.80901699, -0.5, 0.],
             [-0.80901699, 0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0.5, -0.30901699, 0.80901699, 0.],
             [0.30901699, -0.80901699, -0.5, 0.],
             [0.80901699, 0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, 0.80901699, 0.5, 0.],
             [0.80901699, -0.5, 0.30901699, 0.],
             [0.5, 0.30901699, -0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, -0.5, 0.30901699, 0.],
             [-0.5, -0.30901699, 0.80901699, 0.],
             [-0.30901699, -0.80901699, -0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.5, -0.30901699, 0.80901699, 0.],
             [0.30901699, 0.80901699, 0.5, 0.],
             [-0.80901699, 0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0.5, -0.30901699, 0.80901699, 0.],
             [-0.30901699, 0.80901699, 0.5, 0.],
             [-0.80901699, -0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0., 0., 1., 0.],
             [1., 0., 0., 0.],
             [0., 1., 0., 0.],
             [0., 0., 0., 1.]],

            [[0.5, 0.30901699, 0.80901699, 0.],
             [-0.30901699, -0.80901699, 0.5, 0.],
             [0.80901699, -0.5, -0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0., 1., 0., 0.],
             [0., 0., 1., 0.],
             [1., 0., 0., 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, -0.5, -0.30901699, 0.],
             [0.5, 0.30901699, 0.80901699, 0.],
             [-0.30901699, -0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[-0.80901699, -0.5, 0.30901699, 0.],
             [0.5, -0.30901699, 0.80901699, 0.],
             [-0.30901699, 0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, -0.80901699, 0.5, 0.],
             [0.80901699, 0.5, 0.30901699, 0.],
             [-0.5, 0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.5, 0.30901699, 0.80901699, 0.],
             [0.30901699, -0.80901699, 0.5, 0.],
             [0.80901699, 0.5, 0.30901699, 0.],
             [0., 0., 0., 1.]],

            [[0.80901699, 0.5, 0.30901699, 0.],
             [-0.5, 0.30901699, 0.80901699, 0.],
             [0.30901699, -0.80901699, 0.5, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, 0.80901699, -0.5, 0.],
             [-0.80901699, 0.5, 0.30901699, 0.],
             [0.5, 0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[0.30901699, -0.80901699, -0.5, 0.],
             [0.80901699, 0.5, -0.30901699, 0.],
             [0.5, -0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-1., 0., 0., 0.],
             [0., -1., 0., 0.],
             [0., 0., 1., 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, -0.80901699, 0.5, 0.],
             [0.80901699, -0.5, -0.30901699, 0.],
             [0.5, 0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]],

            [[-0.30901699, 0.80901699, 0.5, 0.],
             [-0.80901699, -0.5, 0.30901699, 0.],
             [0.5, -0.30901699, 0.80901699, 0.],
             [0., 0., 0., 1.]]
        ]