I found 4D Golf a great game to explore higher dimensional space.
Steam link: https://store.steampowered.com/app/2147950/4D_Golf
The person goes over quite a few technical details on their Youtube, though they talk about a bunch of other coding experiments too.
[1] https://store.steampowered.com/app/473950/Manifold_Garden/
When I first saw the title, I assumed this game was implemented in the same engine. I believe there are a few already.