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Published online by Cambridge University Press: 23 March 2025
Abstract chiral polytopes are intrinsically combinatorial objects. In this chapter a geometric meaning is given to many of them. This follows the ideas of Grünbaum of skeletal polyhedra. As part of the discussion, chiral polyhedra in Euclidean three-dimensional space are described in a different way from the one in which they were originally found by Schulte. Chiral polytopes of full rank are those that attain a certain upper bound with respect to their dimensions; this is the same bound used to define regular polytopes of full rank. It is proven that chiral polytopes of full rank exist only in ranks 4 and 5. This is an unexpected contrast with regular polytopes of full rank, which exist in every rank.
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