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