The edge-minimal polyhedral maps of Euler characteristic \(-8\)
type: Item
instance of: scholarly article
title: The edge-minimal polyhedral maps of Euler characteristic \(-8\)
zbMATH Open document ID: 1017.52010
author: Basudeb Datta
author: N. Nilakantan
author: Ulrich Brehm
published in: Beiträge zur Algebra und Geometrie
publication date: 2003-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/226358
full work available at URL: 23.html
review text: A polyhedral map \(P\) on a surface \(\mathbb M\) is called \(\{p,q\}\)-equivelar if each face of \(P\) is a \(p\)-gon and the degree of each vertex is \(q\). \textit{U. Brehm} [Topics in combinatorics and graph theory, 153-162 (1990; Zbl 0703.57008)] constructed a \(\{5,5\}\)-equivelar polyhedral map of Euler characteristic \(-8\). In this article the authors prove that for each \(m\geq 2\) there exists a selfdual \(\{5,5\}\)-equivelar polyhedral map on an orientable surface of Euler characteristic \(-4m\) and there exists a selfdual \(\{5,5\}\)-equivelar polyhedral map on a non-orientable surface of Euler characteristic \(-(4m+2)\). Moreover, it is proved that there is a unique \(\{5,5\}\)-equivelar polyhedral map on an orientable surface of Euler characteristic \(-8\).
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 57M20
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1866014
zbMATH Keywords: polyhedral maps
zbMATH Keywords: polyhedral 2-manifold
reviewed by: Stanislav Jendroľ
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1866014