The Platonic Solids occur in conjugate pairs. The Dodecahedron and Icosahedron are one such pair. The Dodecahedron has twelve pentagonal faces and 12x5=60. The Icosaahedron has twenty triangular faces and 3x20=60. THis allows the Dodecahedron to be nested in the Icosahedron and connected with 60 links resulting in a dazzling geometric effect of profound beauty.