The Icosian Game, Revisited

Abstract

In 1857 Sir William Rowan Hamilton invented the Icosian game [1]. In a world based on the dodecahedral graph, a traveler must visit 20 cities, without revisiting any of them. Today, when the trip makes a loop through all the vertices of the graph, it is called a Hamiltonian tour (or cycle). When the first and last vertices in a trip are not connected, it is called a Hamiltonian path (or trail). The first image shown is a tour; the second is a path.