Symmetry Type Graphs of Polytopes and Maniplexes
Por:
Cunningham G., Del Río-Francos M., Hubard I., Toledo M.
Publicada:
1 jun 2015
Categoría:
Discrete Mathematics and Combinatorics
Resumen:
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. © 2015, Springer Basel.
Filiaciones:
Cunningham G.:
University of Massachusetts Boston, 100 Morrissey Blvd., Boston, MA 02125-3393, United States
Del Río-Francos M.:
Institute of Mathematics Physics and Mechanics, University of Ljubljana, Jadranska 19, Ljubljana, SI-1000, Slovenia
Hubard I.:
Univ Nacl Autonoma Mexico, Inst Matemat, Cuernavaca 62210, Morelos, Mexico
Toledo M.:
Univ Nacl Autonoma Mexico, Inst Matemat, Cuernavaca 62210, Morelos, Mexico
All Open Access; Green
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