13 Joints
2We have associated the thirty-one zone star throughout with the icosahedron and the dodecahedron. It also fits perfectly with the three smaller regular polyhedra. The tetrahedron, the cube and the octahedron fit inside the icosahedron and the dodecahedron. Their vertices touch a vertex, an edge midpoint or a face midpoint of the larger figure. This regular match between large and small figure positions the smaller figure so that regular patterns on the large figure project inwards as regular patterns on the small figure. In each case, either five or ten small figures fit at once within the larger figure.1 Each of the regular polyhedra is thus a convenient core from which to define the regular thirty-one zone star. The geometric regularities insure simplicity in the connections. Any one of the regular polyhedra can be used with the same pattern of flanges or holes on each of its faces as a connector for the thirty-one zone structural system.2
