Alright, some brief notes on the construction of a rotating 4D object.
In 3D, vertices are represented by a 3 component coordinate set (x, y, and z). A unit cube has 8 such vertices, and centered at the origin and aligned with the coordinate space the vertices would appear at all combinations of x = +/-0.5, y = +/-0.5, and z = +/-0.5.
In 4D, all vertices have 4 components (x, y, z, w). For a unit cube in 4D, there would be 16 such vertices, with x = +/-0.5, y = +/-0.5, z = +/-0.5, and w = +/-0.5. For other more complex shapes, a fair amount of geometry and trig might be required to figure out what the values of these coordinates are.
To map 3D images to a 2D plane, we project them: objects with a larger distance from the viewer (greater value for the z component) are drawn smaller because they are farther away. A very simple projection from 3D to 2D is to make the new 2D point equal to (x/z, y/z). Granted, for this to work the object needs to be moved in front of the viewer first... using values of z <= zero would cause problems.
To map 4D images to a 3D space we do something similar... points farther away along the w axis are scaled down to appear smaller. Like 3D to 2D, the most simple way to do this mapping is to choose a new 3D point based on (x/w, y/w, z/w), after the object has been translated far enough away from the camera that all values of w are positive.
Now all that is left is to rotate the object in 4D space over time. A more interesting rotation is accomplished by making sure that the w component is one of those influenced by the rotation... otherwise it will just look like a static 3D object rotating in 3D space. The rotation can be accomplished using some simple trigonometry:
current w = cos(angle) * original w + sin(angle) * original z
current z = cos(angle) * original z - sin(angle) * original w
This will result in a simple rotation through the x/y plane (a plane is an axis in 4D, because points that lie on it are not influenced by the rotation).
Now you have all the tools you need to make your own rotating 4D objects (except maybe access to Maya and an understanding of MEL scripting)
