Description
The Minkowski sum of
X and
Y is the polyhedron
X + Y = {x + y  x in X, y in Y}. If
X and
Y are both cones, then their Minkowski sum is their positive hull, which is a cone, so the output is a
Cone. Otherwise the output is a
Polyhedron.
X and
Y have to lie in the same ambient space.
i1 : P1 = convexHull matrix {{0,1,1},{0,1,1}}
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 {{0,1,1},{0,1,1}}
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 : Q = minkowskiSum(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 Q
o4 =  2 2 1 1 1 1 
 0 0 1 1 1 1 
2 6
o4 : Matrix QQ < QQ

See also
Cone + Cone,
Cone + Polyhedron,
Polyhedron + Cone, and
Polyhedron + Cone.