The tomotope - Monson, Barry (Ars mathematica contemporanea, 2012)
Every abstract 3-polytope ?$\mathcal{M}$?, 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 ?$\mathcal{M}$?. Here we demonstrate that the situation for polytopes of higher rank must be very different: the tomotope ?$\mathcal{T}$? is a small, highly involved, abstract uniform 4-polytope. It has infinitely many distinct minimal regular covers.
Keywords: abstract regular polytopes; graph theory; politopi; teorija grafov; uniform polytopes