An engine for multiple dimensions?

Miscellaneous Forums/General Discussion/An engine for multiple dimensions?

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http://www.superliminal.com/cube/cube.htm

^4-dimensional rubic's cube application. And some other examples near the bottom of that page. Of course, it's probably an 'artistic' interpretation of what 4-D looks like. But the math behind it seems plausible, but haven't read too much into it.