## Tumbling Hypercubes Zoetrope #3DxMathematics #3DxAnimation #3DThursday #3DPrinting #3D

Tumbling Hypercubes Zoetrope from Ken Perlin:

We’re still doing production on the little walking guy. But meanwhile my collaborator Eva Schindling and I managed to build a nice little working zoetrope of a tumbling hypercube.

For those of you who don’t know, a hypercube is something like a cube, only with four dimensions instead of three. As a cube is to a square, a hypercube is to a cube. I made a java applet some years back that lets you play with them.

Of course we don’t live in four dimensions, so it’s hard to get a feeling for what happens when you rotate four dimensional things. Eva and I thought that it would be cool, rather than looking at 4D things rotating on a computer screen, to create an animated sculpture of a rotating hypercube. That way you could look around it from all directions (at least, all 3D directions) as it does its weird 4D rotation.

Because a hypercube has four dimensions instead of three, it can rotate in some pretty fancy ways. A simple rotation only requires two dimensions. Since a hypercube has four dimensions, it can rotate one way in two of its dimensions, while rotating a different way in the other two dimensions….

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