Tight orientably-regular polytopes
Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 69-82.

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It is known that every equivelar abstract polytope of type {p1, …, pn − 1} has at least 2p1⋯pn − 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.
DOI : 10.26493/1855-3974.554.e50
Mots-clés : Abstract regular polytope, equivelar polytope, flat polytope, tight polytope 
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Marston D. E. Conder; Gabe Cunningham. Tight orientably-regular polytopes. Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 69-82. doi : 10.26493/1855-3974.554.e50. https://geodesic-test.mathdoc.fr/articles/10.26493/1855-3974.554.e50/

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