specified in a traditional way for polygons, i.e., by the ordered sequence of its vertices . When the input list of vertices (or edges) is unordered, the time complexity of the problems becomes O(m log m). A matching lower bound is known in the algebraic decision tree model of computation. Volume computation The task of computing the volume of a convex polytope has been studied in the field of computational geometry. The volume can be computed approximately, for instance, using the convex volume approximation technique, when having access to a membership oracle. As for exact computation, one obstacle is that, when given a representation of the convex polytope as an equation system of linear inequalities, the volume of the polytope may have a bit-length which is not polynomial in this representation. See also Oriented matroid Nef polyhedron Steinitz's theorem for convex polyhedra References External links Komei Fukuda, Polyhedral computation FAQ. Polytopes Polytope