Characterization of a family of rotationally symmetric spherical quadrangulations

Lowell Abrams, Daniel Slilaty

Abstract


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 dihedral symmetry.


Keywords


Quadrangulation, spherical quadrangulation, rotational symmetry

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DOI: https://doi.org/10.26493/1855-3974.2433.ba6

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications