Metatron's Cube and the Platonic Solids
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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.
Contributed by: Erik Zillner and Lauren Ciardiello (July 2015)
Open content licensed under CC BY-NC-SA
 Wikipedia. "Metatron's Cube." (Jul 6, 2015) en.wikipedia.org/wiki/Metatron%27 s_Cube.
"Metatron's Cube and the Platonic Solids"
Wolfram Demonstrations Project
Published: July 7 2015