Operators over regular maps

Stephen Edwin Wilson

Vol. 81 (1979), No. 2, 559–568

DOI: 10.2140/pjm.1979.81.559

Abstract

In this paper, we define certain operators, each of which transforms one regular map into another. These operator are based on the notions of Petrie path and j-th order “hole” introduced by Coxeter. Together with the usual dual operator, they are a powerful tool for the analysis and taxonomy of regular maps. We produce, as an example, 18 distinct maps from the icosahedron, including six of Brahana and Coble’s eight pentagonal dodecahedra.

Mathematical Subject Classification 2000

Primary: 57M15

Secondary: 05C10

Milestones

Received: 5 October 1977

Revised: 1 June 1978

Published: 1 April 1979