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 $(3,3,3)$ that is a subgroup of index $2$ of the group of symmetries of a toroidal map of type $\{ 6,3\}$.
Categories: math.GR math.AG math.CO