Comparing the constructions of Goldberg, Fuller, Caspar, Klug and Coxeter, and a general approach to local symmetry-preserving operations

DOI10.1098/rspa.2017.0267zbMath1404.52013arXiv1705.02848OpenAlexW2766017291WikidataQ56003536 ScholiaQ56003536MaRDI QIDQ4646862

Gunnar Brinkmann, Stan Schein, Pieter Goetschalckx

Publication date: 28 December 2018

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.02848

zbMATH Keywords

polyhedrachamber systemsymmetry-preservingGoldberg-Coxeter operation

Mathematics Subject Classification ID

Symmetry properties of polytopes (52B15)

Related Items (6)

Weaving patterns inspired by the pentagon snub subdivision scheme ⋮ Construction of fullerenes and Pogorelov polytopes with 5-, 6- and one 7-gonal face ⋮ On local operations that preserve symmetries and on preserving polyhedrality of maps ⋮ The connectivity of the dual ⋮ Local orientation-preserving symmetry preserving operations on polyhedra ⋮ Generation of local symmetry-preserving operations on polyhedra

Cites Work

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• On tilings of the plane
• Goldberg-Coxeter construction for 3- and 4-valent plane graphs
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• Chamfering operation on k-orbit maps
• Mathematical virology: a novel approach to the structure and assembly of viruses
• Wrapping the cube and other polyhedra
• Uniform polyhedra

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