We can look at the stellated cuboctahedron in two different ways:
The stellated cuboctahedron is simply the cube intersected with the octahedron!
We can do this because the cube and the octahedron have a very special relationship with each other: They are duals.
Cube: 6 faces, 8 vertices, 12 edges
Octahedron: 8 faces, 6 vertices, 12 edges
They share many of the same properties  They also share the same polyhedra when they are truncated. To see this, go back and take another look at the Cubocta Family.
