Antonio Montero

Antonio Montero

PhD in mathematics interested in symmetry properties of discrete objects

Chiral extensions of regular toroids

Under review, 2024+

Recommended citation:

A. Montero, M. Toledo. Chiral extensions of regular toroids (preprint). https://arxiv.org/abs/2405.09434.

Preprint here

Abstract: Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational symmetry but do not admit reflections. In this paper we build chiral polytopes whose facets (maximal faces) are isomorphic to a prescribed regular cubic tessellation of the $n$-dimensional torus ($n \geq 2$). As a consequence, we prove that for every $d \geq 3$ there exist infinitely many chiral $d$-polytopes.

Bibtex:

 @Unpublished{MonteroToledo_ChiralExtensionsRegular_preprint,
    author = "Montero, Antonio and Toledo, Micael",
    date = "2024",
    title = "Chiral extensions of regular toroids",
    note = "In preparation",
    abstract = "Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational symmetry but do not admit reflections. In this paper we build chiral polytopes whose facets (maximal faces) are isomorphic to a prescribed regular cubic tessellation of the $n$-dimensional torus ($n \geq 2$). As a consequence, we prove that for every $d \geq 3$ there exist infinitely many chiral $d$-polytopes.",
    keywords = "",
    url = "https://arxiv.org/abs/2405.09434"
}