Minimal equivelar polytopes - Cunningham, Gabe (Ars mathematica contemporanea, 2014)
Every equivelar abstract polytope of type ?$\{p_1,…, p_{n-1}\}$? has at least ?$2p_1,…, 2p_{n-1}$? 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 ?$\{2k_1,…, 2k_{n-1}\}$?.
Keywords: abstract regular polytope; equivelar polytope; flat polytope; mixing