Realizations of regular toroidal maps of type \(\{4,4\}\)
type: Item
instance of: scholarly article
title: Realizations of regular toroidal maps of type \(\{4,4\}\)
zbMATH Open document ID: 0960.51012
published in: Discrete \& Computational Geometry
publication date: 2001-05-10T00:00:00Z
review text: In [Aequationes Math. 37, No. 1, 38-56 (1989; Zbl 0676.51008)], the reviewer introduced a general theory of Euclidean realizations of abstract regular polytopes. In this paper, the authors describe the realization spaces of the regular toroidal polyhedra \(\{4, 4\}_{(b,c)}\), with \(b\geq c\) and \(bc(b-c)=0\). When \(b\geq 2\), the number of non-trivial pure realizations of \(\{4,4\}_{(b,0)}\) is \(r={1\over 2}\lfloor b/2 \rfloor (\lfloor b/2\rfloor +3)\), and when \(c\geq 2\), the number of non-trivial pure realizations of \(\{4,4\}_{(c,c)}\) is \(r'=c+\lfloor c^2/4\rfloor\).
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 1507688
zbMATH Keywords: toroidal polyhedron
zbMATH Keywords: abstract regular polytopes
zbMATH Keywords: realization
author: B. Monson
author: Asia Ivić Weiss
reviewed by: Peter McMullen
MaRDI profile type: Publication
full work available at URL: s004540010048
OpenAlex ID: W1982875144
DOI: 10.1007/S004540010048
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description: scientific article; zbMATH DE number 1507688