PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Constructions for chiral polytopes
Tomaž Pisanski, Marston D. E. Conder and Isabel Hubard
J. Lond. Math. Soc. Volume 77, Number 1, pp. 115-129, 2008. ISSN 0024-6107


An abstract polytope of rank n is said to be chiral if its automorphism group has two orbits on flags, with adjacent flags lying in different orbits. In this paper, we describe a method for constructing finite chiral n-polytopes, by seeking particular normal subgroups of the orientation-preserving subgroup of an n-generator Coxeter group (having the property that the subgroup is not normalized by any reflection and is therefore not normal in the full Coxeter group). This technique is used to identify the smallest examples of chiral 3- and 4-polytopes, in both the self-dual and non-self-dual cases, and then to give the first known examples of finite chiral 5-polytopes, again in both the self-dual and non-self-dual cases.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8265
Deposited By:Boris Horvat
Deposited On:21 February 2012