This moving image of a projection of the four-dimensional 120-cell was made using Stella 4d, software you can try for free here: http://www.software3d.com/stella.php
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Robert, did you have to purchase and pay for the product in order to produce the rotating image?
Yes, and it’s worth it. There is a trial version you can try for free, but saving or printing images requires the fully-functioning version.