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.
compound of five cubes
this was inside the compound of five cubes, sort of an intersection of the five cubes
and this was inside of that previous thing, I think it is a rhombic triacontrahedron (but the dual doesn't look right so maybe not? or maybe the plugin I'm using to generate the duals isn't working right?)
this is a spherical inversion of the compound of five cubes. I'm not sure whether or not there is a name for it?
I thought this might be a disdyakis triacontahedron, but I'm pretty sure it isn't. It is the result of "stellating" the rhombic triacontahedron (actually it looks like there are 227 "full" stellations of the rhombic triacontrahedron? and countless more with more general rules?)