On the Schläfli symbol of chiral extensions of polytopes

Published in Discrete Mathematics, 2021

Recommended citation:

A. Montero. On the Schläfli symbol of chiral extensions of polytopes, Discrete Mathematics (2021). https://doi.org/10.1016/j.disc.2021.112507.

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Abstract: Given an abstract n-polytope K, an abstract (n+1)-polytope P is an extension of K if all the facets of P are isomorphic to K. A chiral polytope is a polytope with maximal rotational symmetry that does not admit any reflections. If P is a chiral extension of K, then all but the last entry of the Schläfli symbol of P are determined. In this paper we introduce some constructions of chiral extensions P of certain chiral polytopes in such a way that the last entry of the Schläfli symbol of P is arbitrarily large.

Bibtex:

 @Article{Montero_2021_SchlaefliSymbolChiral,
    author = "Montero, Antonio",
    title = "On the {Schläfli} symbol of chiral extensions of polytopes",
    doi = "10.1016/j.disc.2021.112507",
    issn = "0012-365X",
    language = "en",
    number = "11",
    pages = "112507",
    url = "https://www.sciencedirect.com/science/article/pii/S0012365X2100220X",
    urldate = "2021-09-17",
    volume = "344",
    abstract = "Given an abstract n-polytope K, an abstract (n+1)-polytope P is an extension of K if all the facets of P are isomorphic to K. A chiral polytope is a polytope with maximal rotational symmetry that does not admit any reflections. If P is a chiral extension of K, then all but the last entry of the Schläfli symbol of P are determined. In this paper we introduce some constructions of chiral extensions P of certain chiral polytopes in such a way that the last entry of the Schläfli symbol of P is arbitrarily large.",
    file = ":Montero\_2021\_SchlaefliSymbolChiral.pdf:PDF",
    journal = "Discrete Mathematics",
    keywords = "Abstract polytopes, Chiral polytopes, Schläfli symbol, research",
    month = "November",
    year = "2021"
}