Re: [math-fun] existence of the icosahedron

Icosahedra? I don't think they exist. [I've been wanting to say that.] I have lately been playing around with strong spherical magnets. One figure that they can make is a very stable icosahedron (12 spheres). A study of the poles on these spheres reveals a very striking 3-fold rotational symmetry. I've been unsuccessful in making the skew cube out of spherical magnets, so far. The dodecahedron seems to be impossible. Several structures do work, and all of them have unexpected polar qualities, so far. --Ed Pegg Jr