The tomotope

Abstract

Every abstract 3-polytope M, in particular, every polyhedral map, has a unique minimal regular cover, and the automorphism group of this cover is isomorphic to the monodromy group of M. Here we demonstrate that the situation for polytopes of higher rank must be very different: the tomotope T is a small, highly involved, abstract uniform 4-polytope. It has infinitely many distinct minimal regular covers.