OK, the ASCII-based 4maze game was a nice diversion, but my heart is always with projections as the "real" way of visualizing 4D, so finally I got off my lazy butt and wrote a program that translates the polytope definitions (with the full lattice meticulously generated by my scripts as I've indicated previously) into something POVRay can render. So here's the first working animation that I made:
http://eusebeia.dyndns.org/~hsteoh/4d/24cell-1.gif
Can anyone guess what this might be? That's right, it's everybody's favorite polytope: the 24-cell, vertex-first perspective projection. The center of the projection, where the octahedral cells meet, is the vertex closest to the 4D viewer.
Note that it is the camera rotating, not the object, so the lighting is also rotating with the object. The rotation is only in 3D, not in 4D (the point is to see the structure of the static projected image). Also, obscured facets (from the 4D POV) are culled, as usual. Not culling obscured facets produces a tangled messy image which is hard to understand, culling them makes the image a lot clearer.