Visualization of Sphere and Horosphere Packings Related to Coxeter Tilings by Simply Truncated Orthoschemes with Parallel Faces

DOI10.31896/K.25.7zbMATH Open1485.52014arXiv2110.14063OpenAlexW4205241896MaRDI QIDQ3390932

Jenő Szirmai, A. Yahya

Publication date: 25 March 2022

Published in: KoG (Search for Journal in Brave)

Abstract: In this paper, we describe and visualize the densest ball and horoball packing configurations belonging to the simply truncated $3$-dimensional hyperbolic Coxeter orthoschemes with parallel faces. These beautiful packing arrangements describe and show the very interesting structure of the mentioned orthoschemes and the corresponding Coxeter groups. We use for the visualization the Beltrami-Cayley-Klein ball model of $3$-dimensional hyperbolic space $$ and the pictures were made by the Python software.

Full work available at URL: https://arxiv.org/abs/2110.14063

zbMATH Keywords

Coxeter grouppackingtilingshyperbolic geometryhorosphere

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Symmetry properties of polytopes (52B15)

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Packings with horo- and hyperballs generated by simple frustum orthoschemes

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