Tight orientably-regular polytopes - Conder, Marston D. E. (Ars mathematica contemporanea, 2015)
It is known that every equivelar abstract polytope of type ?$\{p_1, …, p_{n - 1}\}$? has at least ?$2p_1 … p_{n - 1}$? 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 ?$\{p_1, …, p_{n - 1}\}$?. We show that it is necessary and sufficient that whenever ?$p_i$? is odd, both ?$p_{i - 1}$? and ?$p_{i + 1}$? (when defined) are even divisors of ?$2p_i$?.
Keywords: abstract regular polytope; abstrakten regularen politop; ekvivelaren politop; equivelar polytope; flat polytope; ploščat politop; tesen politop; tight polytope