The tetrahemihexahedron is the only uniform polyhedron that is topologically equivalent to the projective plane. Many other polyhedra having the same topology can be constructed by relaxing the conditions, for example those with faces that are regular polygons but not transitive on the vertices, those with planar faces that are not regular, those with faces that are congruent but non-planar, and so on. Various techniques for generating physical realisations of such polyhedra are discussed, and several examples of different types described. Artists such as Max Bill have explored non-orientable surfaces, in particular the Möbius strip, and Carlo Séquin has considered what is possible with some models of the projective plane. The models described here extend the range of possibilities.