Quotients of a Universal Locally Projective Polytope of type 5,3,5

2003/07/05 by Michael Ian Hartley, Michael I. Hartley, Hartley, Michael Ian +2
Mathematics · #20F65 #51M20 #52B15 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GR #msc:20F65 #msc:51M20 #msc:52B15

paper · pdf · doi:10.48550/arxiv.math/0307075

15 pages, 5 tables, supported in part by the Belgian National Fund for Scientific Research

arxiv created 2003/07/05 · openalex publication_date 2003/07/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article examines the universal polytope \CP (of type \5,3,5\) whose facets are dodecahedra, and whose vertex figures are hemi-icosahedra. The polytope is proven to be finite, and the structure of its group is identified. This information is used to classifiy the quotients of the polytope. A total of 145 quotients are found, including 69 section regular polytopes with the same facets and vertex figures as \CP.

Related

• The Classification of Rank 4 Locally Projective Polytopes and Their Quotients
• A universality theorem for projectively unique polytopes and a conjecture of Shephard
• Hypergraph Polytopes
• Groups of type L₂(q) acting on polytopes
• Problems on Polytopes, Their Groups, and Realizations