About tilings of the type of Penrose of the two-dimensional sphere, which modellings quasicrystals

2018/04/23 by A.S. Prokhoda, Prokhoda, Alexander S.
Business, Management and Accounting · Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Physical sciences #Material Science and Thermodynamics #Materials Science (cond-mat.mtrl-sci) #Optics and Image Analysis

paper · pdf · doi:10.48550/arxiv.1804.08384

openalex publication_date 2018/04/23 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28

Abstract

The problem of constructing a limit series of Penrose type partitions of a two-dimensional sphere is solved, which makes it possible to model quasicrystals possessing a point icosahedral group symmetry Ih. Images of polyhedron models are given (the number of faces for which F> 5000). Based on certain spherical isohedral polyhedra, a recipe is described for constructing spherical polyhedra of Plato, Archimedes, Catalan and Johnson. The boundaries of the chromatic number in the space S2 are established.

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