I was inspired by a still image from the Wikipedia entry on the 24-cell to make an animation of rotating and then stereographically projecting the 24-cell, showing the images of the original polytope edges. Math on Wikipedia is pretty spotty, but the polytope entries have really become top-notch in the last few years.
Here's a still from the animation:
and a medium and small resolution version of the animation:
small (300x300, 6 MB)
medium (512x512, 17 MB).