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The Classification of Rank 4 Locally Projective Polytopes and Their Quotients

Michael I Hartley
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Abstract

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.

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Michael I Hartley. 2004-01-14. The Classification of Rank 4 Locally Projective Polytopes and Their Quotients. https://arxiv.org/abs/math/0310429

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