The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common to the two polyhedra. If the cuboctahedron has unit edge length, the compound can be constructed by midpoint augmentation with heights
(1)
 
(2)

The resulting compound has side lengths
(3)
 
(4)
 
(5)
 
(6)

and surface area and volume
(7)
 
(8)
