Generating the triangulations of the projective plane

A theorem of Steinitz [2] states that the triangulations of the 2-sphere can be generated from the triangulation S with four vertices by a process called vertex splitting. That is, given any triangulation T of the 2sphere, there is a sequence of triangulations S = T,, T, ,..., T,_, , T,, = T, such that each triangulation except T, is obtained from its predecessor by vertex splitting. In this paper we show that the triangulations of the projective plane can be generated by the same process from two particular triangulations of the projective plane.