Tight orientably-regular polytopes

Marston Conder, Gabe Cunningham

Abstract


It is known that every equivelar abstract polytope of type {p1, …, pn − 1} has at least 2p1pn − 1 flags. Polytopes that attain this lower bound are called tight. Here we investigate the conditions under which there is a tight orientably-regular polytope of type {p1, …, pn − 1}. We show that it is necessary and sufficient that whenever pi is odd, both pi − 1 and pi + 1 (when defined) are even divisors of 2pi.


Keywords


Abstract regular polytope, equivelar polytope, flat polytope, tight polytope

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DOI: https://doi.org/10.26493/1855-3974.554.e50

ISSN: 1855-3974

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