A polyhedron of genus 4 with minimal number of vertices and maximal symmetry
type: Item
instance of: scholarly article
title: A polyhedron of genus 4 with minimal number of vertices and maximal symmetry
zbMATH Open document ID: 0673.52004
DOI: 10.1007/BF00147470
author: Jürgen Bokowski
author: Ulrich Brehm
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: The minimal number of vertices v(g) of a triangulation of the orientable 2-manifold of genus g is known [\textit{M. Jungerman} and \textit{G. Ringel}, Acta Math. 145, 121-154 (1980; Zbl 0451.57005)]. In \textit{L. Szilassi}, Topologie Struct. 13, 69-80 (1986; Zbl 0605.52002) and the second author's paper in Mathematika 34, No.2, 237-242 (1987; Zbl 0633.52005) for \(g=1,2,3\) it is shown that for the minimal number V(g) of vertices of a polyhedron of genus g, \(V(g)=v(g)\) holds. In the present paper \(V(4)=v(4)=11\) is proved. Moreover, the extremal polyhedron admits maximal symmetry.
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 4101991
zbMATH Keywords: minimal number of vertices
zbMATH Keywords: triangulation
zbMATH Keywords: extremal polyhedron
zbMATH Keywords: maximal symmetry
reviewed by: Ernest Jucovič
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147470
OpenAlex ID: W2055665178
description: scientific article; zbMATH DE number 4101991