Abstract
We extend the notion of symmetry type graphs of maps to include maniplexes and (abstract) polytopes, using them to study k-orbit maniplexes (where the automorphism group has k orbits on flags). In particular, we show that there are no fully-transitive k-orbit 3-maniplexes with k > 1 an odd number. We classify 3-orbit maniplexes and determine all face transitivities for 3- and 4-orbit maniplexes. Moreover, we give generators of the automorphism group of a maniplex, given its symmetry type graph. Finally, we extend these notions to oriented maniplexes, and we provide a classification of oriented 2-orbit maniplexes and a generating set for their orientation-preserving automorphism group.
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