Conway's Billiard Ball Loop

move

4.

A billiard path is a polygon with vertices on the faces of a polyhedron such that if two segments meet at a vertex

V

on a face

F

, the plane through them is perpendicular to

F

and the angle they form is bisected by the normal to

F

at

V

. A billiard ball loop is a closed billiard path.

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.