Spikey to Wolfram|Alpha Logo
The original Mathematica Spikey was constructed by placing a tetrahedron on each face of an icosahedron. Adding a growing golden octahedron to each face of the icosahedron (which lifts the tetrahedron) gives the rhombic hexecontahedron, the logo of Wolfram|Alpha. In the process, the tetrahedron rotates and its height is reduced by about 5% (this is the difference between a regular tetrahedron and a golden tetrahedron). Growth of octahedra on icosahedra occurs in certain crystals such as boron suboxide.