Medial layer graphs of equivelar 4-polytopes

Authors:
Barry Monson;Asia Ivić Weiss
Affiliations:
University of New Brunswick, Fredericton, New Brunswick, Canada;York University, Toronto, Ontario, Canada
Venue:
European Journal of Combinatorics
Year:
2007

Citing 4
Cited 1

Automorphism groups of symmetric graphs of valency 3

Journal of Combinatorial Theory Series B - Series B
The medial graph and voltage-current duality

Discrete Mathematics
Chirality and projective linear groups

Discrete Mathematics
Self-duality of chiral polytopes

Journal of Combinatorial Theory Series A

Semisymmetric graphs from polytopes

Journal of Combinatorial Theory Series A

Quantified Score

Hi-index	0.00

Visualization

Abstract

In any abstract 4-polytope P, the faces of ranks 1 and 2 constitute, in a natural way, the vertices of a medial layer graph G. We prove that when P is finite, self-dual and regular (or chiral) of type {3, q, 3}, then the graph G is finite, trivalent, connected and 3-transitive (or 2-transitive). Given such a graph, a reverse construction yields a poset with some structure (a polystroma); and from a few well-known symmetric graphs we actually construct new 4-polytopes. As a by-product, any such 2- or 3-transitive graph yields at least a regular map (i.e. 3-polytope) of type {3, q}.