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Article Dans Une Revue Ars Mathematica Contemporanea Année : 2021

Strongly involutive self-dual polyhedra

Résumé

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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Dates et versions

hal-04524630 , version 1 (28-03-2024)

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Javier Bracho, Luis Montejano, Eric Pauli Pérez, Jorge Luis Ramírez Alfonsín. Strongly involutive self-dual polyhedra. Ars Mathematica Contemporanea, 2021, 20 (1), pp.143-149. ⟨10.26493/1855-3974.2194.eab⟩. ⟨hal-04524630⟩
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