Realizations of regular abstract polyhedra of types \(\{3,6\}\) and \(\{6,3\}\)
type: Item
instance of: scholarly article
title: Realizations of regular abstract polyhedra of types \(\{3,6\}\) and \(\{6,3\}\)
zbMATH Open document ID: 0959.51019
author: H. Burgiel
author: D. Stanton
published in: Discrete \& Computational Geometry
publication date: 2000-12-19T00:00:00Z
review text: Regular abstract polyhedra are graded posets which generalize the face lattices of regular polytopes. They also cover non-spherical combinatorial manifolds which admit a flag transitive group action. The authors study a class of regular abstract polyhedra whose boundaries are \(2\)-dimensional tori. These arise as quotients of the regular triangular and hexagonal tilings of the Euclidean plane. The main result classifies geometric realizations of such polyhedra such that the automorphisms are isometries.
reviewed by: Michael Joswig
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1507672
zbMATH Keywords: regular abstract polyhedra
zbMATH Keywords: geometric realizations
zbMATH Keywords: automorphisms
zbMATH Keywords: isometries
MaRDI profile type: Publication
full work available at URL: s004540010030
OpenAlex ID: W2037656870
Wikidata QID: Q56059037
DOI: 10.1007/S004540010030
DBLP publication ID: journals/dcg/BurgielS00
description: scientific article; zbMATH DE number 1507672