Click on this picture to see a movie of two squares rotating in four dimensions. These squares are opposite faces of a cube.

Click on this picture to see a movie of a cube rotating in four dimensions. The cube extends in the x direction, but not in the w direction, so the cube looks like a segment in the x,w plane.

This picture is often a little more difficult to digest at first glance than the previous images, so you may want to take a look at the squares again if it doesn't make sense.

The cube looks like it is turning inside out, as it rotates. This demonstrates how a rigid 3d object can be transformed into its mirror image by moving it through four dimensional space.

Olaf Holt 3/14/94