Über die Symmetriegruppen von regulärseitigen Polytopen. (On the symmetry groups of regular faced polytopes)
type: Item
instance of: scholarly article
title: Über die Symmetriegruppen von regulärseitigen Polytopen. (On the symmetry groups of regular faced polytopes)
zbMATH Open document ID: 0712.52011
DOI: 10.1007/BF01308665
author: G. Blind
author: Roswitha Blind
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178439
review text: Convex polytopes are called regular faced, if all their facets are regular. It is known [\textit{N. W. Johnson}, Can. J. Math. 18, 169-200 (1966; Zbl 0132.146), \textit{V. A. Zalgaller}, Semin. Math. V. A. Steklov. Math. Inst., Leningrad (1969); translation from Zap. Nauk Semin. Leningrad. Otd. mat. Inst. Steklov 2, 1-221 (1967; Zbl 0165.563)] that all regular faced 3-polytopes have a nontrivial symmetry group. Here it is shown, that there exist regular faced d-polytopes with trivial symmetry group, but only for \(d=4\). The corresponding class of polytopes is studied.
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 4171851
zbMATH Keywords: 600-cell
zbMATH Keywords: regular faced d-polytopes
zbMATH Keywords: symmetry group
MaRDI profile type: Publication
cites work: Q3879871
cites work: Q5672665
cites work: Q5547252
cites work: Convex Polyhedra with Regular Faces
cites work: Q5566967
description: scientific article; zbMATH DE number 4171851