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arXiv · 2008.00862

Icosahedral Tiling with Dodecahedral Structures

Mehmet Koca·Ramazan Koc·Nazife Ozdes Koca·Abeer Al-Siyabi
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Abstract

Icosahedron and dodecahedron can be dissected into tetrahedral tiles projected from 3D-facets of the Delone polytopes representing the deep and shallow holes of the root lattice D_6. The six fundamental tiles of tetrahedra of edge lengths 1 and \tau are assembled into four composite tiles whose faces are normal to the 5-fold axes of the icosahedral group. The 3D Euclidean space is tiled face-to-face by the composite tiles with an inflation factor \tau generated by an inflation matrix. The aperiodic tiling is a generalization of the Tubingen triangular tiling in 2-dimensions for the faces of the tiles are made of Robinson triangles. Certain combinations of the tiles constitute dodecahedra with edge lengths of 1 and the golden ratio \tau=(1+\sqrt(5))/2.

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Mehmet Koca, Ramazan Koc, Nazife Ozdes Koca, Abeer Al-Siyabi. 2020-08-03. Icosahedral Tiling with Dodecahedral Structures. https://arxiv.org/abs/2008.00862

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