Chiral polytopes arising from almost-simple groups with socle PSL(2, q)

In terms of their symmetries, not many geometric objects have received more attention than polytopes. Since ancient times, polytopes have been considered with great interest, not only for aesthetic reasons, but also for scientific reasons. More recently, the theory of abstract polytopes, which generalises the concept of classical polytopes, has emerged as a powerful tool for studying symmetries. In the last decade, efforts to classify highly symmetric polytopes, including chiral and regular ones, have highly increased. Given a group ", a lot has been done in order to enumerate all polytopes of a certain type and which have " as their group of symmetries. Many results have been obtained for almost simple groups and atlases for small groups have been drawn up. However, not much is known about chiral polytopes, which are polytopes that have all possible rotational symmetries but no reflections. The purpose of this thesis is to investigate the almost simple groups with socle PSL(2, q), and to determine when they are automorphism groups of chiral polytopes. Furthermore, a comparison between regularity and chirality has emerged as a natural question. Accordingly, we also compare our results to those obtained for regularity.

Name thesis:degree_name

PhD

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

ResearchSpace@Auckland

Year dc:date.issued

2017

Author dc:creator

• Moerenhout, Jeremie

Advisors dc:contributor.advisor

• Leemans, D
• Conder, M

Statement dc:rights

• Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.

Licence dc:rights.uri

• https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm

Handle dc:identifier.uri

https://hdl.handle.net/2292/32579

OAI identifier oai:identifier

oai:researchspace.auckland.ac.nz:2292/32579