THE ICOSAHEDRON PUZZLE.
(Unicursal and Route Problems
The icosahedron is another of the five regular, or Platonic, bodies
having all their sides, angles, and planes similar and equal. It is
bounded by twenty similar equilateral triangles. If you cut out a piece
of cardboard of the form shown in the smaller diagram, and cut half
through along the dotted lines, it will fold up and form a perfect
Now, a Platonic body does not mean a heavenly body; but it will suit the
purpose of our puzzle if we suppose there to be a habitable planet of
this shape. We will also suppose that, owing to a superfluity of water,
the only dry land is along the edges, and that the inhabitants have no
knowledge of navigation. If every one of those edges is 10,000 miles
long and a solitary traveller is placed at the North Pole (the highest
point shown), how far will he have to travel before he will have visited
every habitable part of the planet--that is, have traversed every one of
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