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Maximally symmetric polyhedral realizations of Dyck's regular map

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Ulrich Brehm
Ulrich Brehm
Affiliation:
FB 3-Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 1000 Berlin 12, West-Germany.
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Abstract

We construct realizations of Dyck's regular map of genus three as polyhedra in ℝ3. One of these has one axis of symmetry of order three and three axes of symmetry of order two. The other polyhedra have three axes of symmetry. We show that a polyhedron realizing Dyck's regular map cannot have a symmetry group of order larger than six. Thus the symmetry groups of our realizations are maximal.

MSC classification

Secondary: 52A37: Other problems of combinatorial convexity
Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 229 - 236
Copyright
Copyright © University College London 1987

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