The Icosian game made the vertex-visit puzzle tangible. The report of its 1857 presentation describes a plane projection of a regular dodecahedron, with holes at the vertices for ivory pins. The Trinity College Dublin archive connects this game with the search for closed routes visiting each vertex exactly once. This puzzle supplies a historical illustration of the Hamilton cycle requirement.[ref]
The Icosian Calculus, Hamilton papers archive. The Icosian Calculus, Hamilton papers archive: opening historical introduction and quoted report of the 1857 British Association presentation: dodecahedron projection and ivory pins
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The Icosian Game is a mathematical and combinatorial puzzle created by the British mathematician Sir William Rowan Hamilton in 1857. It involves finding a Hamiltonian path or cycle in a polyhedron's graph structure, specifically related to the vertices of an icosahedron. In the game, players are tasked with finding a route that visits each of the 12 vertices of a regular icosahedron exactly once and returns to the starting point.