Generating polyhedral quadrangulations of the projective plane

Abstract

We determine the 26 families of irreducible polyhedral quadrangulations of the projective plane under three reductions called a face-contraction, a 4 -cycle removal and a 2 3 -path shrink, which were first given by Batagelj in 1989. Every polyhedral quadrangulation of the projective plane can be obtained from one of them by a sequence of the inverse operations of the reductions.