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