The degrees of toroidal regular proper hypermaps

Maria Fernandes; Claudio Alexandre Piedade

doi:10.26493/2590-9770.1350.c36

Maria Fernandes University of Aveiro, Portugal https://orcid.org/0000-0001-7386-4254
Claudio Alexandre Piedade University of Aveiro, Portugal https://orcid.org/0000-0002-0746-5893

DOI: https://doi.org/10.26493/2590-9770.1350.c36

Keywords: Regular polytopes, regular toroidal maps, regular toroidal hypermaps, permutation groups

Abstract

Recently the classification of all possible faithful transitive permutation representations of the group of symmetries of a regular toroidal map was accomplished. In this paper we complete this investigation on a surface of genus 1 considering the group of a regular toroidal hypermap of type (3, 3, 3).