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What is Convex Regularly Faceted Polyhedrons

The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
Convex three-dimensional polytopes whose faces are regular polygons.
Published in Chapter:
Regularly Faceted Three-Dimensional Polytopes
DOI: 10.4018/978-1-7998-8374-6.ch002
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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Polytopes Dual to Higher-Dimensional Polytopes
Convex three-dimensional polytopes whose faces are regular polygons.
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