Conway's Billiard Ball Loop

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A billiard path is a polygon with vertices on the faces of a polyhedron such that if two segments meet at a vertex on a face , the plane through them is perpendicular to and the angle they form is bisected by the normal to at . A billiard ball loop is a closed billiard path.

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This Demonstration shows a loop of a billiard ball in a regular tetrahedron discovered by J. H. Conway. Each vertex is a vertex of a triangle on a face with side length one-tenth the length of an edge of the tetrahedron. There are three such loops.

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Contributed by: Izidor Hafner (October 2013)
Open content licensed under CC BY-NC-SA


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Reference

[1] D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin Books, 1991 p. 14.



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