Metatron's Cube and the Platonic Solids

This Demonstration displays the different 3D Platonic solids that can formed from a 2D configuration called Metatron’s cube. Metatron’s cube (also called “the fruit of life”) is composed of 13 identical circles with lines connecting the centers of all the circles. Two-dimensional projections of the five Platonic solids can be fitted to the pattern. The vertices of the dodecahedron and icosahedron require some off-center points, but in a 3D generalization, using spheres rather than circles, all the vertices will lie at the centers of spheres.