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:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg07l-1Zz-x4uT8S31KzPL0dcNVDwvEmtZ4ti_VYDfxEgxGR3WVsGiA6nFxsdv_MoWMjSOCQNbj_2o86gXWtqTVLsroIUB1ylUWJKRJ1jYHGtjhgo73rSTRtgPwBXDWoiZRgECiRrJxF055/s400/24cellcurved_t20000.png)
and a medium and small resolution version of the animation:
small (300x300, 6 MB) medium (512x512, 17 MB).