As you know, there are actually six convex regular polytopes instead of four. Unfortunately, however, when attempting to construct these, the polygon count was far too much of a strain on Desmos to even be worth all the lag that followed, not to mention the detail of these shapes make it difficult to follow the geometry of each polygon visually.

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Because of these obstacles, I decided not to build the 120-cell and 600-cell, however you can view their animations found on Wikipedia here.