2012/06/08 by Mark Mixer, Mixer, Mark, Egon Schulte +4
Computer Science · Engineering · Mathematics · #51M20 #52B15 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #math.CO #math.MG #msc:51M20 #msc:52B15
paper · pdf · doi:10.48550/arxiv.1206.1647
Discrete Geometry and Applications (eds. R.Connelly and A.Ivic Weiss), Fields Institute Communications, (23 pp, to appear)
arxiv created 2012/06/08 · openalex publication_date 2012/06/08 · arxiv updated 2012/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.