The problem of finding a Hamiltonian Circuit along the edges of an Icosahedron, i.e., a path such that every vertex is visited a single time, no edge is visited twice, and the ending point is the same as the starting point.
See also Hamiltonian Circuit, Icosahedron
Herschel, A. S. ``Sir Wm. Hamilton's Icosian Game.'' Quart. J. Pure Applied Math. 5, 305, 1862.