Tight orientably-regular polytopes
Conder, Marston ; Cunningham, Gabe
ARS MATHEMATICA CONTEMPORANEA, Tome 9 (2014), / Harvested from ARS MATHEMATICA CONTEMPORANEA
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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.

Publié le : 2014-01-01
DOI : https://doi.org/10.26493/1855-3974.554.e50 
@article{554,
     title = {Tight orientably-regular polytopes},
     journal = {ARS MATHEMATICA CONTEMPORANEA},
     volume = {9},
     year = {2014},
     doi = {10.26493/1855-3974.554.e50},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/554}
}

Conder, Marston; Cunningham, Gabe. Tight orientably-regular polytopes. ARS MATHEMATICA CONTEMPORANEA, Tome 9 (2014) . doi : 10.26493/1855-3974.554.e50. http://gdmltest.u-ga.fr/item/554/