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.

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Published

2021-09-02

Issue

Vol. 20 No. 1 (2021)

Section

Articles

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/