So the other night I started working on making a compound of five cubes, which has a “convex hull” of a dodecahedron, meaning, if you were to “shrink wrap” it the result would be a dodecahedron. I had already placed the cubes a long time ago, so I went back to make them into one coherent object, which involved getting the intersections from all the cubes.

While doing that I noticed that the intersections formed an interesting object too, and it looks slightly familiar (I’ve probably looked at hundreds of these things by now), but I haven’t been able to identify it yet. I think it’s a stellation of rhombic triacontahedron. Then while doing that I noticed the inside was yet another interesting object, which I thought it is a rhombic triacontahedron (though the dual doesn’t look right for some reason?). So then I “stellated” that thing and I thought maybe I had a disdyakis triacontahedron (which might be the weirdest named thing I’ve made yet), but upon further inspection I’ve determined it isn’t that. (I think the pointy parts are too pointy; it has the right number of vertices, edges, & faces though. The dual definitely wasn’t right.)

At that point I started thinking I might be developing some kind of polyhedra bug. Now I plan to try making fancy versions of some of these for 3D printing, like the objects here: stellated polyhedra derivatives. More recently I made a tetrahedron-based version.