# Micael Toledo: Maniplexes and the 2-orbit problem

Date: 12. 6. 2017

Source: Discrete mathematics seminar

Source: Discrete mathematics seminar

Torek, 13.6. 2017, od 10h do 12h, Plemljev seminar, Jadranska 19

**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.