Regular pseudo-oriented maps and hypermaps of low genus

Pseudo-orientable maps were introduced by Wilson in 1976 to describe non-orientable regular maps for which it is possible to assign an orientation to each vertex in such a way that adjacent vertices have opposite orientations. This property extends naturally to non-orientable and orientable hypermaps. In this paper we classify the regular pseudo-oriented maps and hypermaps of characteristic χ⩾−3χ⩾−3. With the help of GAP (The GAP group, 2014) and its library of small groups, we extend the classification down to characteristic χ=−16χ=−16 (Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18 and Table 19 in the Appendix).