Around Dodecahedron In 20 Points*


by W. R. Hamilton

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The graph in the circle in the illustration is a two-dimensional projection on the plane of a dodecahedron (a three-dimensional solid with twelve pentagonal faces). Each green point on the graph represents the respective vertex of the dodecahedron, and each white line between any two points - the respective edge. Such graphs, which project some three-dimensional problems and puzzles onto the two-dimensional plane, are called Schlegel diagrams.

The object of this puzzle is to visit all the 20 green points on the graph. You can start at any point but you may visit each point only once. Moving from point to point you have to travel along the white lines (alleys) only. You have to finish at the point where you've started your journey from.

*This puzzle is an Icosian game which was invented by the mathematician W. R. Hamilton in 1859. Hamilton devised a branch of mathematics to solve similar path-tracing problems on two-dimensional solids. He called it Icosian calculus.

Posted: December 11, 2007
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