 Because these order simplices are all congruent to each other and (for orders on formula_1 elements) there are formula_54 different linear orders, the volume of each order simplex is formula_55.More generally, an order polytope can be partitioned into order simplices in a canonical way, with one simplex for each linear extension of the corresponding partially ordered set.Therefore, the volume of any order polytope is formula_55 multiplied by the number of linear extensions of the corresponding partially ordered set.