We construct a hierarchical tiling of 3 dimensional Euclidean space based on a triangular prism, using repeated rotations, about orthogonal axes, by angles 2π/m and 2π/n. To analyze the structure of the tiling we are led to determine the group G(m,n) generated by such a pair of rotations, for m=n=3 and for m=3, n=4.
KeywordsEuclidean Space Dimensional Euclidean Space Orthogonal Axis Triangular Prism Repeated Rotation
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