Micael Toledo: Maniplexes and the 2-orbit problem

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