2 - A Pure Mathematical Creation?

The icosahedron is the subtlest of the Platonic solids:

Tetrahedron Octahedron Icosahedron Cube Dodecahedron

Benno Artmann wrote:

The original knowledge of the dodecahedron may have come from crystals of pyrite, but in contrast the icosahedron is a pure mathematical creation.... It is the first realization of an entity that existed before only in abstract thought. (Well, apart from the statues of gods!)

The Platonic solid pictures are from the Wikipedia article on Platonic solids.

Quote from:

Benno Artmann, About the cover: the mathematical conquest of the third dimension, Bulletin of the AMS, 43 (2006), 231-235.

For more information see:

Benno Artmann, Euclid — The Creation of Mathematics, Springer, New York, second ed., 2001. (The material on the icosahedron is not in the first edition.)
Benno Artmann, Antike Darstellungen des Ikosaeders, Mitt. DMV 13 (2005), 45-50.

The picture of an iron pyrite crystal is from Hershel Friedman's webpage on Pyrite, part of his website called The Mineral and Gemstone Kingdom.