Every equivelar abstract polytope of type ▫$\{p_1,\dots, p_{n-1}\}$▫ has at least ▫$2p_1,\dots, 2p_{n-1}$▫ 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 ▫$\{2k_1,\dots, 2k_{n-1}\}$▫.
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