Polytopes of high rank for the alternating groups

Authors:
Maria Elisa Fernandes;Dimitri Leemans;Mark Mixer
Affiliations:
Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal;Université Libre de Bruxelles, Département de Mathématiques, C.P. 216 Géométrie, Bld du Triomphe, 1050 Bruxelles, Belgium;Université Libre de Bruxelles, Département de Mathématiques, C.P. 216 Géométrie, Bld du Triomphe, 1050 Bruxelles, Belgium
Venue:
Journal of Combinatorial Theory Series A
Year:
2012

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Abstract

There is a well-known correspondence between abstract regular polytopes and string C-groups. In this paper, for each d=3, a string C-group with d generators, isomorphic to an alternating group of degree n is constructed (for some n=9), or equivalently an abstract regular d-polytope, is produced with automorphism group Alt(n). A method that extends the CPR graph of a polytope to a different CPR graph of a larger (or possibly isomorphic) polytope is used to prove that various groups are themselves string C-groups.