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OldPolyhedra :: volume

volume -- computes the volume of a polytope

Synopsis

Description

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

Ways to use volume :

For the programmer

The object volume is a method function.