Geodesic
Characterization of a family of rotationally symmetric spherical quadrangulations
Ars mathematica contemporanea, Tome 22 (2022) no. 2, article no. 10, 35 p. Cet article a éte moissonné depuis la source Ars Mathematica Contemporanea website

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A spherical quadrangulation is an embedding of a graph G in the sphere in which each facial boundary walk has length four. Vertices that are not of degree four in G are called curvature vertices. In this paper we classify all spherical quadrangulations with n-fold rotational symmetry (n ≥ 3) that have minimum degree 3 and the least possible number of curvature vertices, and describe all such spherical quadrangulations in terms of nets of quadrilaterals. The description reveals that such rotationally symmetric quadrangulations necessarily also have a pole-exchanging symmetry.
DOI : 10.26493/1855-3974.2433.ba6
Keywords: Quadrangulation, spherical quadrangulation, rotational symmetry 
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Lowell Abrams; Daniel Slilaty. Characterization of a family of rotationally symmetric spherical quadrangulations. Ars mathematica contemporanea, Tome 22 (2022) no. 2, article  no. 10, 35 p.. doi: 10.26493/1855-3974.2433.ba6

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