Operations on maniplexes and oriented maniplexes

In the past we have been using flag graphs and symmetry type graphs for studying certain operations on maps and their symmetries, such as truncation, dual, medial, chamfering, etc. Here we study similar operations on oriented maps. Certain new operations that can only be defined for oriented maps, such as snub, are considered. In the oriented case the primary tools, i.e. flag graphs and symmetry type graphs, are substituted by arc graphs and oriented symmetry type graphs. Same ideas apply to operations on maniplexes and oriented maniplexes and henceforth to polytopes and oriented polytopes. In particular, it is shown that the “twist” operation that Steve Wilson introduced in his talk in Veszprem is naturally defined on oriented maniplexes rather than orientable ones. The talk will be presented using Sage. This is work in progress with Leah Berman,  Gordon Williams and Steve Wilson.