Polytopes with Preassigned Automorphism Groups

2015/05/23 by Egon Schulte, Schulte, Egon, Gordon Williams +2
Mathematics · #51M20 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #Primary 52B15 #Secondary 52B11 #math.CO #math.MG #msc:51M20 #msc:52B11 #msc:52B15

paper · pdf · doi:10.48550/arxiv.1505.06253

Discrete & Computational Geometry (to appear)

arxiv created 2015/05/23 · openalex publication_date 2015/05/23 · arxiv updated 2015/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show that this abstract polytope may be realized as a convex polytope.

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