Higher Toroidal Regular Polytopes

Abstract/quad A regular polytope is locally toroidal if its minimal sections which are not of spherical type are toroids. The locally toroidal polytopes of rank 4 have been extensively discussed, and their classification is now nearly complete. In this paper, the locally toroidal polytopes of higher rank are investigated. Again, an almost complete classification of these regular polytopes is obtained; as well as sporadic examples, there are several infinite families