An existence result on two-orbit maniplexes

Abstract

A maniplex of rank n is a connected, n-valent, edge-coloured graph that generalises abstract polytopes and maps. If the automorphism group of a maniplex M partitions the vertex-set of M into k distinct orbits, we say that M is a k-orbit n-maniplex. The symmetry type graph of M is the quotient pregraph obtained by contracting every orbit into a single vertex. Symmetry type graphs of maniplexes satisfy a series of very specific properties. The question arises whether any pregraph of order k satisfying these properties is the symmetry type graph of some k-orbit maniplex. We answer the question when k = 2.