Stereographic Projection of Platonic Solids
This Demonstration shows the stereographic projection of the five Platonic solids.[more]
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.[less]
 J. Leys, E. Ghys, and A. Alvarez. "Dimensions." (Jul 17, 2012) www.dimensions-math.org/Dim_reg_E.htm.