Self-duality of chiral polytopes

Authors:
Isabel Hubard;Asia Ivić Weiss
Affiliations:
York University, Toronto, Ont, Canada M3J 1P3;York University, Toronto, Ont, Canada M3J 1P3
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

Citing 3
Cited 3

A non-involutory selfduality

Discrete Mathematics
Chirality and projective linear groups

Discrete Mathematics
Determination of all regular maps of small genus

Journal of Combinatorial Theory Series B

Semisymmetric graphs from polytopes

Journal of Combinatorial Theory Series A
Medial layer graphs of equivelar 4-polytopes

European Journal of Combinatorics
Constructing self-dual chiral polytopes

European Journal of Combinatorics

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Abstract

We prove that self-dual chiral polytopes of odd rank possess a polarity, that is, an involutory duality, and give an example showing this is not true in even ranks. Properties of the extended groups, that is of the groups of automorphisms and dualities, of self-dual chiral polytopes are discussed in detail.