Stereographic Projection of Platonic Solids

This Demonstration shows the stereographic projection of the five Platonic solids.
To understand stereographic projection, imagine that on top of the unit sphere there is a light and that the sphere is sitting on a plane. Any point on the surface of the sphere casts a shadow onto this plane, which is called the stereographic projection of the point. Now take a Platonic solid and blow up its edges until they lie on the sphere's surface. The stereographic projection of the Platonic solid is the shadow these lines cast onto the plane.
  • Contributed by: Emile Okada
  • (Mathematica Summer Camp 2012)

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Reference
[1] J. Leys, E. Ghys, and A. Alvarez. "Dimensions." (Jul 17, 2012) www.dimensions-math.org/Dim_reg_E.htm.
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