the octahedron, twenty in the dodecahedron, and twelve in the icosahedron. If we add to these three figures the regular tetrahedron, which we have had frequent occasion to study, and the cube (which is represented, at least in outline, in the skeleton of the hexactinellid sponges), we have completed the series of the five regular polyhedra known to geometers, the Platonic bodies84 of the older mathematicians. It is
at first sight all the more remarkable that we should here meet {480} with the whole five regular polyhedra, when we remember that, among the vast variety of crystalline forms known among minerals, the regular