Polytopes with preassigned automorphism groups
type: Item
instance of: scholarly article
title: Polytopes with preassigned automorphism groups
zbMATH Open document ID: 1357.52018
author: Egon Schulte
author: Gordon Williams
published in: Discrete \& Computational Geometry
publication date: 2015-12-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/1505.06253
review text: The main results of the paper under review read as follows: Theorem 1. Every finite group is the automorphism group of a finite abstract polytope. In particular, if \(\Gamma\) is isomorphic to a subgroup of the symmetric group \(S_{n+1}\), then there exists a finite abstract polytope \(\mathcal{P}\) of rank \(d\), \(d\leqslant n\), with automorphism group \(\Gamma\) such that \(\mathcal{P}\) is isomorphic to a face-to-face tessellation of the \((d-1)\)-sphere by topological copies of convex \((d-1)\)-polytopes. Theorem 2. The abstract polytope \(\mathcal{P}\) may be realized convexly.
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B15
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 6515544
zbMATH Keywords: convex polytope
zbMATH Keywords: abstract polytope
zbMATH Keywords: automorphism group
zbMATH Keywords: barycentric subdivision
zbMATH Keywords: combinatorical theory of convex polytopes
reviewed by: Victor Alexandrov
MaRDI profile type: Publication
OpenAlex ID: W1555300770
arXiv ID: 1505.06253
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DOI: 10.1007/S00454-015-9710-1
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description: scientific article