[cgufus]

Cool, Thanks. To me, 4-D rotation is completely “unpredictable” or “contraintuitive”, or both. I wonder, you as a developer of that visualization, did you get an intuition for it? do you know in advance how the projection changes when you apply one or the other rotation?

[tehsauce]

I did actually! As jcun2148 pointed out, the game of trying to return the hyper cube to the start position is a great way to start building intuition. To describe what each rotation axis does in words: There are six axes of rotation because there are 6 perpendicular planes in 4D (xy, xz, xw, yz, yw, zw). The 3 of these which only use xyz are just the regular axes of rotation. The other three rotate between a regular axis and the 4th dimension. This has the effect of a kind of toroidal wrapping (you may have animations of this, where the inner cubes wrap around to become the outer cube) oriented in the direction of the other xyz coordinate.