  This article announces the completion of the classification of rank 4 locally
projective polytopes and their quotients. There are seventeen universal locally
projective polytopes (nine nondegenerate). Amongst their 441 quotients are a
further four (nonuniversal) regular polytopes, and 152 nonregular but section
regular polytopes. All 156 of the latter have hemidodecahedral facets or
hemi-icosahedral vertex figures. It is noted that, remarkably, every rank 4
locally projective section regular polytope is finite. The article gives a
survey of the literature of locally projective polytopes and their quotients,
and fills one small gap in the classification in rank 4.
