Minimal equivelar polytopes

Gabe Cunningham


Every equivelar abstract polytope of type {p1, …, pn − 1} has at least 2p1pn − 1 flags. In this paper, we study polytopes that attain this lower bound, called tight polytopes. Using properties of flat polytopes, we are able to give a complete local characterization of when a polytope is tight. We then show a way to construct tight polyhedra of type {p, q} when p and q are not both odd, and a way to construct regular tight polytopes of type {2k1, …, 2kn − 1}.


abstract regular polytope; equivelar polytope; flat polytope; mixing

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ISSN: 1855-3974

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