
The cuboctahedron
The cuboctahedron is, among the Archimedean solids, the only one whose radius (the distance from its center to its vertices) equals the length of its edges. This means that rods could be used to join its vertices with a central ball. As it has 12 vertices, as many as 12 rods could be used. The result is the reinforced cuboctahedron shown in the lefthand picture.
These inner rods also show that the inner space of the cuboctahedron could be split into eight regular tetrahedra (corresponding to its eight triangular faces) and six square pyramids (corresponding to its six square faces). If we fill each tetrahedron with four balls, we will get the object shown in the righthand picture, a very good paperweight at more than 500 grams.
By doubling the scale of the tetrahedra, the cuboctahedron is also doubled:
We can also make a «Sierpinski cuboctahedron», just by building it with Sierpinski tetrahedra:
