Problem of the Week 1159

Cubic Billiards

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Find a billiard path inside a cube that

1. starts at a point on a face of the cube;
2. visits all the faces;
3. returns to its starting point; and
4. never strikes an edge or corner of the cube.

The path should be viewed as an ideal light ray that stays inside the cube, reflecting off faces in the usual way that preserves angles. The path should never strike a corner or edge.

Source: Such a path was first discovered by Hugo Steinhaus. Spotted in The Penguin Dictionary of Curious and Interesting Geometry by David Wells.

© Copyright 2012 Stan Wagon. Reproduced with permission.

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