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

- Operator: +
- Usage:
    `Q = P + C`
- Inputs:
  - P, a convex polyhedron
  - C, a convex rational cone
- Outputs:
  - Q, a convex polyhedron

## 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.

See also minkowskiSum.

    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

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:7934:0.