It is very easy to build a rhombitruncated cuboctahedron around a rhombicuboctahedron.

One can choose between building twelve cubes on the square faces which share edges with triangular faces (option A, left-hand picture), or building eight cupolas on the triangular faces (option B, right-hand picture):

In both cases, the only remaining edges are four alternate ones for each of the six octagonal faces:

The hollow hexagonal faces could be reinforced by means of six rods or three rods and three rhombuses. For bigger strength, a regular tetrahedron could be built on each of the triangular faces of the original rhombicuboctahedron; its upper vertex is the same as the center ball in the hexagon:

Lastly, twelve square panels could be added in order to close the cubes built on the faces of the inner rhombicuboctahedron:

Because of its geometry, the rhombitruncated cuboctahedron can be used to build giant models of the tetrahedron, the cube, and the octahedron. In these cases, we will use the reinforced version.