Antonio Montero

Antonio Montero

PhD in mathematics interested in symmetry properties of discrete objects

Regular polyhedra in the 3-torus

Published in Advances in Geometry, 2018

Recommended citation:

A. Montero. Regular polyhedra in the 3-torus, Advances in Geometry (2018). https://doi.org/10.1515/advgeom-2018-0017.

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Abstract: In this paper we discuss the classification rank $3$ lattices preserved by finite orthogonal groups and derive from it the classification of regular polyhedra in the $3$-dimensional torus. This classification is closely related to the classification of regular polyhedra in the $3$-space.

Bibtex:

 @Article{Montero_2018_RegularPolyhedra3,
    author = "Montero, Antonio",
    title = "Regular polyhedra in the 3-torus",
    doi = "10.1515/advgeom-2018-0017",
    issn = "1615-715X",
    number = "4",
    pages = "431--450",
    volume = "18",
    abstract = "In this paper we discuss the classification rank $3$ lattices preserved by finite orthogonal groups and derive from it the classification of regular polyhedra in the $3$-dimensional torus. This classification is closely related to the classification of regular polyhedra in the $3$-space.",
    file = ":Montero\_2018\_RegularPolyhedra3.pdf:PDF",
    journal = "Advances in Geometry",
    keywords = "52B15 (51M20 52B10), research",
    mrnumber = "3871407",
    year = "2018"
}