3D Billiard Loop in a Rectangular Box

This Demonstration shows a path of a billiard ball in a 3D box that returns to its starting point, hitting each face once.
This is equivalent to a light beam looping inside a mirror box.

SNAPSHOTS

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DETAILS

To ensure a closed path in a rectangular box, the direction from the starting point (red point) needs to be parallel to a space diagonal.
Since the path does not depend on the coordinate system, all parts of the path are parallel to one space diagonal.
The length of the path is twice the length of a space diagonal.
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