The Minkowski sum 
of two sets 
and 
in a vector
space is given by 
.
The Minkowski sum of two disks centered at 
and 
with radii 
and 
, respectively, is given by the disk centered at 
with radius 
. The Minkowski sum of two balls
is given similarly.
If 
and 
are polyhedra, then 
is a polyhedron and every
extreme point of 
is the sum of an extreme point in 
and an extreme point in 
. For example, taking the Minkowski sums of the following pairs
of Platonic solids in dual
position but with unit edge lengths give the following polyhedra.
 ,  |  |
| regular tetrahedron and regular tetrahedron | cuboctahedron |
| cube and regular octahedron | small rhombicuboctahedron |
| regular dodecahedron and regular icosahedron | small rhombicosidodecahedron |
The Minkowski sum operation is implemented in the Wolfram Language as RegionDilation.
