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1 results

  • 6 - Skeletal Polytopes

  • Daniel Pellicer, Universidad Nacional Autónoma de México
  • Book:
    Abstract Chiral Polytopes
    Published online:
    23 March 2025
    Print publication:
    03 April 2025, pp 342-448

  • Summary

    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.