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.