Johnny Brainwash and I have stumbled upon that nice bit of esoterica as well.

As the platonic solids had a cult based around them, and the icosahedron was the esoteric inner secret:

wikipedia:

"The 12 edges of a regular octahedron can be subdivided in the golden ratio so that the resulting vertices define a regular icosahedron. This is done by first placing vectors along the octahedron's edges such that each face is bounded by a cycle, then similarly subdividing each edge into the golden mean along the direction of its vector. The five octahedra defining any given icosahedron form a regular polyhedral compound, as do the two icosahedra that can be defined in this way from any given octahedron."

'Course, we figured the inner secret was an Illuminatus Prestige Class.