Hereditary Polytopes

TL;DR

This paper introduces hereditary polytopes, a class extending regular polytopes, exploring their properties, construction, and potential applications, with a focus on those with highly symmetric faces.

Contribution

It develops the foundational theory of hereditary polytopes, including methods for analyzing and constructing those with highly symmetric faces, expanding understanding beyond regular polytopes.

Findings

Hereditary polytopes generalize regular polytopes by inheriting facet symmetries.

The paper provides construction techniques for hereditary polytopes with symmetric faces.

Hereditary polytopes have potential applications in structural modeling.

Abstract

Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular polytopes are by definition hereditary, but the other polytopes in this class are interesting, have possible applications in modeling of structures, and have not been previously investigated. This paper establishes the basic theory of hereditary polytopes, focussing on the analysis and construction of hereditary polytopes with highly symmetric faces.