2020/05/08 by Bracho, Javier, Montejano, Luis, Pauli, Eric +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.03866
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.