The faces of five particular polyhedra have a special quality: they allow for the alternating of adjacent faces in checkerboard fashion. Because of this binary property these polyhedra can
each be assembled using permanent magnets, like refrigerator magnets, polarized with north on one face and south on the other. The polygon
magnets must be oriented so that those with north poles facing out have neighbors with south poles facing out.

Octahedron
8 triangle magnets

Small rhombicosidocahedron
62 magnets