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What is Mechanical Operations on a Polyhedron

The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
Conceivable transformations of a polyhedron, including cutting a polyhedron (cutting off vertices), deforming a section of a cut to obtain a regular polygon in a section, rotating parts of a polyhedron after cutting relative to each other.
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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Regular and Semi-Regular Three-Dimensional Polytopes
?ass="highlight">onceivable transformatiass="highlight">ons of a polyhedrass="highlight">on, including cutting a polyhedrass="highlight">on (cutting off vertices), deforming a sectiass="highlight">on of a cut to obtain a regular polygass="highlight">on in a sectiass="highlight">on, rotating parts of a polyhedrass="highlight">on after cutting relative to each other.
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Polytopes Dual to Higher-Dimensional Polytopes
Cass="highlight">onceivable transformatiass="highlight">ons of a polyhedrass="highlight">on, including cutting a polyhedrass="highlight">on (cutting off vertices), deforming a sectiass="highlight">on of a cut to obtain a regular polygass="highlight">on in a sectiass="highlight">on, rotating parts of a polyhedrass="highlight">on after cutting relative to each other.
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