The Wolfram|Alpha logo is the rhombic hexecontahedron, a 60-faced polyhedron. It is the of 227 fully supported stellations of the rhombic triacontahedron (30-faced solid). The stellation is the cube 5-compound. Historically, Kepler seems to have been the first to look at some of these stellations. Coxeter found a few more in 1948. In 1958, John Ede described 13 of them . In 1978, G. S. Pawley seems to have been the first to describe them all . Only 32 of the 227 stellations are given.
J. D. Ede, "Rhombic Triacontahedra," Mathematical Gazette 42, 1958 pp. 98-100.
G. S. Pawley, "The 227 Triacontahedra," Geometriae Dedicata 4, 1975 pp. 221-232.