Hereditary Polytopes
Combinatorics
2012-06-11 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1206.1647,
title = {Hereditary Polytopes},
author = {Mark Mixer and Egon Schulte and Asia Ivic Weiss},
journal= {arXiv preprint arXiv:1206.1647},
year = {2012}
}
Comments
Discrete Geometry and Applications (eds. R.Connelly and A.Ivic Weiss), Fields Institute Communications, (23 pp, to appear)