Strongly involutive self-dual polyhedra

Javier Bracho, Luis Montejano, Eric Pauli Pérez, Jorge Luis Ramírez-Alfonsín

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.


Keywords


Self-dual, polyhedra, graph, 3-connected, duality.

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

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications