 Under this representation, the edges of the polytope connect comparable elements of the lattice.If two functions formula_59 and formula_60 both belong to the order polytope of a partially ordered set formula_3, then the function formula_62 that maps formula_31 to formula_64,
and the function formula_65 that maps formula_31 to formula_67 both also belong to the order polytope.The two operations formula_68 and formula_69 give the order polytope the structure of a continuous distributive lattice, within which the finite distributive lattice of Birkhoff's theorem is embedded.