I did this to see how accurate of a point cloud I could get with a complicated geometric shape.
Affectionately known as the "Wolfram|Alpha spikey," this 3D object has many interesting mathematical properties. It is a polyhedron with 60 identical faces, 62 verticies and 120 edges, known as a rhombic hexecontahedron. Its 20 outer points form the verticies of a regular dodecahedron; its 12 inner points form the verticies of a regular icosahedron. Each of its faces is a golden rhombus, with four equal sides, and diagonals with lengths in the golden ration of ~1.618. One might think that such an elegant geometrical object must have been known since antiquity, but in fact is seems to have first been explicitly constructed only in 1940, and rediscovered several times even more recently. It can however be produced by stellating the rhombic triacontahedron which was constructed by Kepler around 1611. When 12 of these triacontahedra are packed together (as in some natural quasicrystals), they leave a gap in the center that is in the shape of the Wolfram|Alpha log.