Billiard in a 4D Hypercube

This Demonstration shows a billiard ball inside a 4D hypercube; the ball travels in straight lines and bounces off the 3D hyperfaces. To understand the principle, we proceed by analogy:
• In a square in 2D, the ball bounces against one of the four edges bounding the square.
• In a cube in 3D, the ball bounces against one of the six square faces bounding the cube.
• In a hypercube in 4D, the ball bounces against one of the eight cubic hyperfaces bounding the 4D hypercube.

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