One thing is for sure: You've seriously screwed up on the icosahedron.

Apparently you misinterpreted the positions of the individual points,
probably thinking that Phi<1, but in fact Phi>1.

Swapping the 1's and Phi's in the TwentyHedron definition gives a nice
regular icosahedron.

You also got the front top cap's ordering of points wrong. Fixing that
will give you a nicely textured mesh.


As for the union of individual triangles, I'm still working on that one;
I must confess that so far I don't really have a clue where things go wrong.

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