# Reflexible maps and hypermaps with face–stabilisers pointwise stabilising half the faces

@article{dAzevedo2002ReflexibleMA,
title={Reflexible maps and hypermaps with face–stabilisers pointwise stabilising half the faces},
author={Ant{\'o}nio Breda d'Azevedo},
journal={Journal of Geometry},
year={2002},
volume={73},
pages={93-111}
}
Abstract. This paper deals mainly with reflexible hypermaps in which the stabiliser of a hyperface fixes exactly half the hyperfaces - these reflexible hypermaps are called here 2-dichromatic. The number $F({\cal H})$ of hyperfaces of any 2-dichromatic hypermap $\cal H$ must be necessarily even and greater than or equal to 4. We prove that if $F({\cal H})=2n>4$ then $\cal H$ is necessarily orientable and of type $(4a,4b,{nc\over 2})$, for some positive integers $a$, $b$ and… CONTINUE READING