Semisymmetric graphs from polytopes

Authors:
Barry Monson;Tomaž Pisanski;Egon Schulte;Asia Ivić Weiss
Affiliations:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada;University of Ljubljana, FMF Jadranska 19, Ljubljana 1111, Slovenia and Faculty of Education, University of Primorska, Cankarjeva 5, Koper 6000, Slovenia;Department of Mathematics, Northeastern University, Boston, MA 02115, USA;Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

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Abstract

Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edge- but not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.