Geometric realization of a triangulation on the projective plane with one face removed
Let M be a map on a surface F(2). A geometric realization of M is an embedding of F(2) into a Euclidean 3-space R(3) such that each face of M is a flat polygon. We shall prove that every triangulation G on the projective plane has a face f such that the triangulation of the Mobius band obtained from G by removing the interior of f has a geometric realization.
geometric realization triangulation projective plane mobius band