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The movie shows the stereographic projection of a rotating four dimensional cube onto a three dimensional hyperplane. Imagine the cube as a wire frame in three dimensions. The picture you see on the screen is an additional projection onto a two-dimensional plane. This adds another perspective to the picture. The shadow is effectively the other dimension.



Here you can view an interactive 4d cube, enjoy!!!

http://www.superliminal.com/cube/applet.html