@aaroneous, I really like this build and look forward to seeing what you do with it. I’m with @scruffynerf here - since the radius is essentially fixed, full 3D is not really necessary. I think I’d first play with a 2D spherical mapping. The network idea would be fun too.
Coming tomorrow - small update to Pixel Teleporter so folks can experiment with mappings/patterns for this sort of shape without having the physical object at hand.
I’m being Mr. Lazy Geometry Person at this point and just supplying some basic tools. A full on Archimedean/Catalan solid library would be awesome, but it’s some distance down the project list right now.