"The Symmetry of Things" by Conway, Burgiel, and Goodman-Strauss. You can see the various names it goes by in this photo, which is a page out of that book. This page is the direct inspiration for this beadwork. More so, it's a recipe for how all of the loops fit together.
Now that it's done, I'm pretty sure what I beaded is called an omnitruncated 120-cell on Wikipedia. Fritz Obermeyer created and gifted this image into the public domain. Isn't it pretty?
I didn't bead anywhere near that entire mathematical object, but I did bead a little chunk of it. In fact, I only finished one of the 120 of the (4.6.10). The weird thing about beading this object is you can just keep adding more and more loops and more and more polygons. It feels a lot like beading the infinite skew polyhedron faujasite because they share many of the same shapes connected in the same ways. However, faujasite is an infinite 3D structure, and this is a finite 4D structure. And in this thing, the angles don't work correctly in 3D. To see what I mean, look at all of the distortion in that blue image above. Everything in the center is squished, and everything near the outside is all stretched out. So you couldn't bead the whole thing the way I beaded mine here. But we can bead lots of different chunks of it. I definitely could have kept going. The challenge as an artist is to decide where to stop.
here in my Etsy shop. Thanks for looking.