Constructions for chiral polytopes
نویسندگان
چکیده
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 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 3and 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. Research supported in part by the N.Z. Marsden Fund, Grant UOA 412 Joint position at the University of Primorska, Koper. Research supported in part by the Ministry of Higher Education, Science and Technology of Slovenia, Grants P1-0294,J1-6062,L1-7230.
منابع مشابه
Constructing self-dual chiral polytopes
An abstract polytope is chiral if its automorphism group has two orbits on the flags, such that adjacent flags belong to distinct orbits. There are still few examples of chiral polytopes, and few constructions that can create chiral polytopes with specified properties. In this paper, we show how to build self-dual chiral polytopes using the mixing construction for polytopes.
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