Reflexible maps and hypermaps with face-stabilisers pointwise stabilising half the faces (Q1610986)

The notion of a hypermap is a generalization of the classical notion of a map on a surface. Roughly it is a decomposition of a surface into polygonal cells. For the distinction between topological and algebraic hypermaps see also \textit{D. Corn} and \textit{D. Singerman} [Eur. J. Comb. 9, 337-351 (1988; Zbl 0665.57002)]. The paper deals with reflexible hypermaps, i.e., such with a flag transitive automorphism group. This continues previous work by the author in [The reflexible hypermaps of characteristic \(-2\), Math. Slovaca 47, 131-153 (1997)]. In the present paper the author investigates a partial classification of those reflexible hypermaps in which the stabiliser of a hyperface fixes exactly half the hyperfaces.