Polyhedra have a dual.
Of the Platonoiic solids there are cube/octahedron, the icosahedron/dodecahedron, and the sef dual tetrahedron. Plus: there is an interesting concoction of a cube and an octahedron called a cuboctahedron, with a dual of a rhombic dodecahedron. Here are 2 photos of a octahedron inside a cube inside a cuboctahedron inside a rhombic dodecahedron.
(The last one hasnt got its bottom 4 rods because the balls are too large to enable it to wrap round completely, though I guess it would do if the balls and rods were thin.)