# volume -- computes the volume of a polytope

## Synopsis

• Usage:
v = volume P
• Inputs:
• P, , , which must be compact
• Outputs:
• v,

## 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 = P o1 : Polyhedron i2 : volume P 4 o2 = - 3 o2 : QQ

## Ways to use volume :

• "volume(Polyhedron)"

## For the programmer

The object volume is .