  A Cayley hyperdigraph is a directed hypergraph that its automorphism group
contains a subgroup acting regularly on vertices and a Cayley hypermap is a
hypermap whose automorphism group contains a subgroup which induces regular
action on the hypervertex set. In this paper, we study Cayley hyperdigraphs and
construct Cayley hypermaps which have high level of symmetry. Our main goal is
to present the general theory so as to make it clear to study Cayley hypermaps.
