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Regularly Faceted Three-Dimensional Polytopes

Regularly Faceted Three-Dimensional Polytopes

Copyright: © 2022 |Pages: 44
ISBN13: 9781799883746|ISBN10: 1799883744|ISBN13 Softcover: 9781799883753|EISBN13: 9781799883760
DOI: 10.4018/978-1-7998-8374-6.ch002
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MLA

Gennadiy Vladimirovich Zhizhin. "Regularly Faceted Three-Dimensional Polytopes." The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems, IGI Global, 2022, pp.20-63. https://doi.org/10.4018/978-1-7998-8374-6.ch002

APA

G. Zhizhin (2022). Regularly Faceted Three-Dimensional Polytopes. IGI Global. https://doi.org/10.4018/978-1-7998-8374-6.ch002

Chicago

Gennadiy Vladimirovich Zhizhin. "Regularly Faceted Three-Dimensional Polytopes." In The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems. Hershey, PA: IGI Global, 2022. https://doi.org/10.4018/978-1-7998-8374-6.ch002

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Abstract

It is shown that known classification of convex polyhedrons with sides from correct polygons offered by V.A. Zallgaller as full transfer of all possible convex figures of this type is far from completeness. There exist nine new convex polyhedrons with sides from correct polygons and the impossibility of existence of two figures from Zallgeller classification. Thus, the general number of regularly faceted polyhedrons except for the regular polyhedrons, known semiregular polyhedrons, prisms, and antiprisms make 100 figures instead of 92 as Johnson earlier assumed. The existence of a convex polyhedron with faces of regular polygons was discovered, which differs as much as possible from the bodies of Archimedes and Plato by the presence of six different types of gonohedrons in it (polytypichedron-max).

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