 The order polytope is a distributive polytope, meaning that coordinatewise minima and maxima of pairs of its points remain within the polytope.The order polytope of a partial order should be distinguished from the "linear ordering polytope", a polytope defined from a number formula_1 as the convex hull of indicator vectors of the sets of edges of formula_1-vertex transitive tournaments.A partially ordered set is a pair formula_3 where formula_4 is an arbitrary set and formula_5 is a binary relation on pairs of elements of formula_4 that is reflexive (for all formula_7, formula_8), antisymmetric (for all formula_9 with formula_10 at most one of formula_11 and formula_12 can be true), and transitive (for all formula_13, if formula_11 and formula_15 then formula_16).