# Polyhedron + Polyhedron -- computes the Minkowski sum of two polyhedra

• Operator: +
• Usage:
Q = P1 + P2
• Inputs:
• P1,
• P2,
• Outputs:

## Description

Computes the Minkowski sum of P1 and P2.This is the polyhedron P1 + P2 = {x + y | x in P1, y in P2}. Note that P1 and P2 have to lie in the same ambient space.

 i1 : P1 = convexHull matrix {{1,0,0},{0,1,0}} o1 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 3 number of rays => 0 number of vertices => 3 o1 : Polyhedron i2 : P2 = convexHull matrix {{-1,0,0},{0,-1,0}} o2 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 3 number of rays => 0 number of vertices => 3 o2 : Polyhedron i3 : P = P1 + P2 o3 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 6 number of rays => 0 number of vertices => 6 o3 : Polyhedron i4 : vertices P o4 = | -1 1 0 1 0 -1 | | 0 0 -1 -1 1 1 | 2 6 o4 : Matrix QQ <--- QQ