Hypermaps and symmetry
Hypermaps and symmetry
The most familiar regular polyhedra in R3 are the five Platonic solids. These are examples of regular hypermaps with Platonic automorphism group (group of symmetries of a Platonic solid). The purpose of this thesis is to obtain topological descriptions of all the regular hypermaps with a given automorphism or rotation group. The main chapter is Chapter III in which we give a more detailed description of the regular hypermaps with Platonic automorphism groups, using branched coverings and operations. To help with this description a catalogue of the small regular hypermaps (i.e. with 2p blades, p prime) is obtained in Chapter II. In Chapter I we review the general theory of topological and algebraic hypermaps extending it to hypermaps of non-finite type. From Chapter II to Chapter V we classify the regular hypermaps with Abelian, Dihedral (Dn, n odd), Platonic, PSL(2,7), PSL(2,9), Delta(4,4,3), Delta(3,3,3) and Delta(3,2,6) automorphism group, and with Cyclic, Platonic and Binary rotation group. Finally, in Chapter VI, we give a brief outline of the main results and discuss the existence of regular hypermaps on surface with a given genus.
University of Southampton
Breda d'Azevedo, Antonio Joao de Castilho
1991
Breda d'Azevedo, Antonio Joao de Castilho
Breda d'Azevedo, Antonio Joao de Castilho
(1991)
Hypermaps and symmetry.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The most familiar regular polyhedra in R3 are the five Platonic solids. These are examples of regular hypermaps with Platonic automorphism group (group of symmetries of a Platonic solid). The purpose of this thesis is to obtain topological descriptions of all the regular hypermaps with a given automorphism or rotation group. The main chapter is Chapter III in which we give a more detailed description of the regular hypermaps with Platonic automorphism groups, using branched coverings and operations. To help with this description a catalogue of the small regular hypermaps (i.e. with 2p blades, p prime) is obtained in Chapter II. In Chapter I we review the general theory of topological and algebraic hypermaps extending it to hypermaps of non-finite type. From Chapter II to Chapter V we classify the regular hypermaps with Abelian, Dihedral (Dn, n odd), Platonic, PSL(2,7), PSL(2,9), Delta(4,4,3), Delta(3,3,3) and Delta(3,2,6) automorphism group, and with Cyclic, Platonic and Binary rotation group. Finally, in Chapter VI, we give a brief outline of the main results and discuss the existence of regular hypermaps on surface with a given genus.
This record has no associated files available for download.
More information
Published date: 1991
Identifiers
Local EPrints ID: 460611
URI: http://eprints.soton.ac.uk/id/eprint/460611
PURE UUID: 50a0f7d4-b264-4bc7-a37a-854657ea1a8f
Catalogue record
Date deposited: 04 Jul 2022 18:25
Last modified: 04 Jul 2022 18:25
Export record
Contributors
Author:
Antonio Joao de Castilho Breda d'Azevedo
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics