Strongly involutive self-dual polyhedra

Authors

  • Javier Bracho Instituto de Matemáticas UNAM, Mexico
  • Luis Montejano UNAM-Campus Juriquilla, Mexico
  • Eric Pauli Pérez UNAM-Campus Juriquilla, Mexico and University of Montpellier, France
  • Jorge Luis Ramírez Alfonsín University of Montpellier, France

DOI:

https://doi.org/10.26493/1855-3974.2194.eab

Keywords:

Polyhedra, graphs, duality, self-dual, antipodal

Abstract

A polyhedron is a graph G which is simple, planar and 3-connected. In this note, we classify the family of strongly involutive self-dual polyhedra. The latter is done by using a well-known result due to Tutte characterizing 3-connected graphs. We also show that this special class of polyhedra self-duality behaves topologically as the antipodal mapping. These self-dual polyhedra are related with several problems in convex and discrete geometry including the Vázsonyi problem.

Published

2021-09-02

Issue

Section

Articles