Classification of primer hypermaps with a prime number of hyperfaces

A (face-)primer hypermap is a regular oriented hypermap with no regular proper quotients with the same number of hyperfaces. Primer hypermaps are then regular hypermaps whose automorphism groups induce faithful actions on their hyperfaces. In this paper we classify the primer hypermaps with a prime number of hyperfaces. This classification generalises an earlier dual classification by Du, Kwak and Nedela of regular oriented maps with a prime number of vertices and simple underlying graph.