Strongly involutive self-dual polyhedra
Combinatorics
2020-05-11 v1
Abstract
A polyhedron is a graph 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 V\'azsonyi problem.
Cite
@article{arxiv.2005.03866,
title = {Strongly involutive self-dual polyhedra},
author = {Javier Bracho and Luis Montejano and Eric Pauli and Jorge Luis Ramirez Alfonsin},
journal= {arXiv preprint arXiv:2005.03866},
year = {2020}
}