In my early post concerning pseudodesics, it was found that to have a structural frame work that provides omni-triangulation, but with a minimum of different parts, would be very desirable from an economy standpoint. Fuller’s Fly’s Eye is a great example of economy, but the fabrication of precision fiberglass hyperbolic saddles is a little daunting for anyone with out access to a well ventilated area.
It would be even more advantageous if those economical parts could be manufactured in a small space to begin with, as not everyone has access to a machine shop. Surely there must exist a solution (or two or …infinity).
Fortunately for us, there are shapes provided by dear old Nature that are cataloged as Johnson solids. All edge-lengths are the same. My. Goodness. They’re even ready-equipped with truncations! It’s a rather happy stroke of luck. I think I am particularly impressed with the diminished rhombicosidodecahedron. Look at all those square faces, perfect for windows! The pentagons could easily be developed further into pentagonal pyramids, for increased structural strength if so desired.
Yes, I think we’re on to something here.
If we were to go the full Fly’s Eye treatment here, we need not use the diminished from of the rhombicosidodecahedron, but the full version, skinny legs and all.