How would things work out if we conceive of a 3-D billiards, theoretically speaking? I imagine it would be equivalent to a 4-D torus. Does the dichotomy extend to higher dimensions too?

## 3-D billiards

How would things work out if we conceive of a 3-D billiards, theoretically speaking? I imagine it would be equivalent to a 4-D torus. Does the dichotomy extend to higher dimensions too?