# Icosian Game

The Icosian Game is a game devised by William Hamilton and first described by him in 1857 at a meeting of the British Association in Dublin. The object of the game is to find a way around the edges of a dodecahedron so that every vertex (corner) is visited once and only once. A path such as this became known as a Hamilton circuit, though the task of finding a circuit that passes just once through every vertex of a shape seems to have arisen first in connection with Leonhard Euler's study of the knight's tour. Two years before Hamilton introduced his game, Thomas Kirkman posed the problem explicitly in a paper that he submitted to the Royal Society: Given a graph of a polyhedron, does there exist a cycle passing through every vertex?

The Icosian Game stemmed from Hamilton's invention of a curious kind of
algebra that he called *icosians*, based on the symmetry properties
of the icosahedron. Hamilton connected the
mathematics of his icosians with the problem of traveling along the edges
of a dodecahedron, hitting each vertex just once, and coming back to the
starting point. His friend and fellow Irishman John Graves (1806–1870)
suggested turning the problem into a commercial game and put Hamilton in
contact with the London company of John Jacques and Sons, toy-makers and
manufacturer of high quality chess sets. Jacques bought the rights to the
game for £25 and marketed two versions of it, under the name *Around the
World*. One version, for the parlor, was played on a flat board; another,
for the "traveler," consisted of an actual dodecahedron. In both cases,
nails at each vertex stood for a major city of the world and the player
wrapped a piece of string around these nails as they went. In the event,
the game was a complete sales flop, mainly because it was too easy, even
for children – but not for Hamilton himself who always used the icosian
calculus to figure out his moves, instead of just trying different paths
like everyone else!