The construction of self-dual projective polyhedra (Q1322000)

A projective polyhedra is a simple graph embedded in the projective plane such that the union of the closures of any two faces is either disconnected or simply connected. Equivalently, a projective polyhedra is a 3-connected graph embedded in the projective plane such that any noncontractible cycle intersects the graph in at least three points. Any embedded graph has a natural geometric dual. In this paper we examine projective polyhedra which are isomorphic (as embedded graphs) to their duals. We give two constructions of such self-dual projective polyhedra. We then show that any self-dual projective polyhedron arises from one of these two constructions.