Preserving and Increasing Symmetries of Polyhedral Maps

Gunnar Brinkmann, Fabio Buccoliero, Heidi Van den Camp*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this article we investigate the question which local symmetry preserving operations can not only preserve, but also increase the symmetry of a polyhedral map, e.g. modelling spherical or toroidal fullerenes. Often operations that can increase symmetry, can nevertheless not do so for polyhedral maps of every genus. So for maps that can increase symmetry, we also investigate for which genera they can do so. We give complete answers for operations with inflation factor at most 6 (that is: that increase the number of edges by a factor of at most 6) and for the chemically relevant Goldberg-Coxeter operations and the leapfrog operation.

Original languageEnglish
Pages (from-to)131-161
Number of pages31
JournalMatch
Volume93
Issue number1
DOIs
Publication statusPublished - 2025

Bibliographical note

Publisher Copyright:
© 2025 University of Kragujevac, Faculty of Science. All rights reserved.

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