Amafirlian: this ranks with your cube as a jaw-dropper!
I cannot believe I've never noticed this before - I even used a dodecahedron one time as a support strutures for the five tetrahedra, and still missed it.
I've just seen it, and even though I should go to bed I gotta go build it. Also, scribbling as we speak to calculate how close this is.
We really must come up with a ranking system on the wikia: how about if we start with a single new category "5star" which is simply added to the article. We could encourage attribution. I'll try it here and see how it feels.
--Karl Horton 09:08, 9 August 2007 (UTC)
This is how I came up with it: I started out looking for a support structure. The experience I had with the penrose tiling made me look at connecting the 5-pointed star with a pentagon one rod deeper. It looked very promising so I took the idea back to the computer and built a CAD model using a mix of SpringDance and Sketchup. It became clear that this solution has intersecting rods. But when I looked at that one, I recognised a pattern from my earlier five intersecting tetrahedra. I never expected it to work though, but out of curiousity I calculated how much it would be off (using measured distances in my SpringDance model), and to my amazement it came down to about 2.98 where you need 3! So I immediately went to work to build it.
--Amafirlian 16:20, 10 August 2007 (UTC)
This looks really interesting, haven't had chance to build it yet but hopefully I can have a go this weekend.
I have a way to build an externally supported Rhombic Triacontahedron which is completely accurate, it's quite fragile though and tricky to build. I'll try and get some pictures and an article together.
--Chillum 12:11, 11 August 2007 (UTC)
Looking forward to see it!
--Amafirlian 12:18, 11 August 2007 (UTC)
It might be a while.. new job + new girlfriend means I don't have too much time for Geomag at the moment.. can't complain though :)
--Chillum 16:47, 11 August 2007 (UTC)
Hey, I just discovered another version of an internally supported rhombic triacontahedron. It's not yet photographed, but is trivially easy to build and uses exactly the same number of rods.
I've never seen this called out before, unbelievably, because its so obvious.
So here's the prescription: Start with an icosahedron, and erect pyramids on each face, that's your internal support. Now, place "starfish" pieces over each of the 12 icosahedron vertices, connecting to the points of the 20 pyramids.
Its by no means as elegant as this one (the rhombii aren't as good, and the 3-vertexes are fragile) but good to have side by side!
--Karl Horton 15:48, 22 January 2009 (UTC)