Characterization of a Family of Rotationally Symmetric Spherical Quadrangulations

Authors

Lowell Abrams
Daniel Slilaty, Wright State University - Main CampusFollow

Document Type

Article

Publication Date

5-27-2022

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 a pole-exchanging symmetry.

Comments

This work is licensed under CC BY 4.0

Repository Citation

Abrams, L., & Slilaty, D. (2022). Characterization of a Family of Rotationally Symmetric Spherical Quadrangulations. ARS Mathematica Contemporanea, 22 (2).
https://corescholar.libraries.wright.edu/math/466

DOI

10.26493/1855-3974.2433.ba6