Equivelar Toroids with Few Flag-Orbits

Published in Discrete \& Computational Geometry, 2021

Recommended citation:

J. Collins, A. Montero. Equivelar Toroids with Few Flag-Orbits, Discrete \& Computational Geometry (2021). https://doi.org/10.1007/s00454-020-00230-y.

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Abstract: An $$(n+1)$$(n+1)-toroid is a quotient of a tessellation of the n-dimensional Euclidean space with a lattice group. Toroids are generalisations of maps on the torus to higher dimensions and also provide examples of abstract polytopes. Equivelar toroids are those that are induced by regular tessellations. In this paper we present a classification of equivelar $$(n+1)$$(n+1)-toroids with at most n flag-orbits; in particular, we discuss a classification of 2-orbit toroids of arbitrary dimension.

Bibtex:

 @Article{CollinsMontero_2021_EquivelarToroidsFew,
    author = "Collins, José and Montero, Antonio",
    title = "Equivelar {Toroids} with {Few} {Flag}-{Orbits}",
    doi = "10.1007/s00454-020-00230-y",
    issn = "1432-0444",
    language = "en",
    number = "2",
    pages = "305--330",
    url = "https://doi.org/10.1007/s00454-020-00230-y",
    urldate = "2021-02-18",
    volume = "65",
    abstract = "An \$\$(n+1)\$\$(n+1)-toroid is a quotient of a tessellation of the n-dimensional Euclidean space with a lattice group. Toroids are generalisations of maps on the torus to higher dimensions and also provide examples of abstract polytopes. Equivelar toroids are those that are induced by regular tessellations. In this paper we present a classification of equivelar \$\$(n+1)\$\$(n+1)-toroids with at most n flag-orbits; in particular, we discuss a classification of 2-orbit toroids of arbitrary dimension.",
    file = ":CollinsMontero\_2021\_EquivelarToroidsFew.pdf:PDF",
    journal = "Discrete \\& Computational Geometry",
    keywords = "research",
    month = "January",
    year = "2021"
}