Geodesic
Minimal equivelar polytopes
Ars Mathematica Contemporanea, Tome 7 (2014) no. 2, pp. 299-315.

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Every equivelar abstract polytope of type {p1, …, pn − 1} has at least 2p1⋯pn − 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}.
DOI : 10.26493/1855-3974.357.422
Keywords: abstract regular polytope, equivelar polytope, flat polytope, mixing 
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Gabe Cunningham. Minimal equivelar polytopes. Ars Mathematica Contemporanea, Tome 7 (2014) no. 2, pp. 299-315. doi : 10.26493/1855-3974.357.422. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.357.422/

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