First, a cuboctahedron.
Next, its dual, the rhombic dodecahedron.
And, after that, the icosidodecahedron.
And finally, its dual, the rhombic triacontahedron.
All of these rotating images were assembled using Stella 4d, available at http://www.software3d.com/Stella.php.
Whoa! That is amazing. You leave me in the dust, RobertLovesPi.
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Well, thank you! This sort of thing is actually what you’ll find more of on this blog than anything else. I’ve taken a break from my usual topic — polyhedra — since you started following my blog.