volume computes the volume of a polytope. To do this, it triangulates the polytope first. The volume of a simplex is |det(v_1-v_0,..,v_n-v_0)|/n!, where v_0,..,v_n are the vertices of the simplex.
i1 : P = crossPolytope 3 o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 8 number of rays => 0 number of vertices => 6 o1 : Polyhedron |
i2 : volume P 4 o2 = - 3 o2 : QQ |
The object volume is a method function.