## 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

icosahedron.

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

the edges?

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INSPECTING A MINE.
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THE FLY ON THE OCTAHEDRON.