Bicontactual regular maps
type: Item
instance of: scholarly article
title: Bicontactual regular maps
zbMATH Open document ID: 0583.05024
author: Steve Wilson
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: This paper is not self-contained, as the reader is directed to a predecessor [the author, Pac. J. Math. 81, 559-568 (1979; Zbl 0433.05021)] six years removed for almost all key concepts. This is particularly unfortunate, as an important part of the author's terminology is not standard. Specifically, a map M is a 2-cell imbedding of a (necessarily connected) graph into a (possibly nonorientable) closed 2-manifold. A flag is a mutual incidence of vertex, edge, and face. If the automorphism group of M is transitive on flags, M is said to be regular (many authors say ''reflexible''). A rotary map has an automorphism group containing all vertex and face rotations (many authors say ''regular'' or ''symmetrical'' here). A rotary map may fail to be regular, in which case it is chiral. In this paper the author classifies all rotary maps with the property that each face meets only one or two others. He shows that all such maps are in fact regular and that they are closed under the action of four operators: D (for dual), P (for Petrie), opp (for opposite), and \(H_ j\) (for \(j^{th}\) order hole) - all defined in the earlier paper. These facts are then used to prove: Every non-trivial rotary map whose number of edges is a power of 2 is orientable.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 3933098
zbMATH Keywords: rotary maps
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: pjm.1985.120.437
OpenAlex ID: W2063369997
DOI: 10.2140/PJM.1985.120.437
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description: scientific article; zbMATH DE number 3933098