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# Polyhedron + Cone -- computes the Minkowski sum of a polyhedron and a cone

## Synopsis

• Operator: +
• Usage:
Q = P + C
• Inputs:
• Outputs:

## Description

Computes the Minkowski sum of P and C. This is the polyhedron P + C = {p + c | p in P, c in C}. Note that P and C have to lie in the same ambient space.

 i1 : P = hypercube 2 o1 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o1 : Polyhedron i2 : C = posHull matrix {{1},{2}} o2 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of the cone => 1 number of facets => 1 number of rays => 1 o2 : Cone i3 : Q = P + C o3 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 1 number of vertices => 3 o3 : Polyhedron i4 : (vertices Q,rays Q) o4 = (| -1 1 -1 |, | 1 |) | -1 -1 1 | | 2 | o4 : Sequence