Platonic Balls

I keep myself pretty anonymous online.  Its deliberate really.
And then i go to AU, and write my secret identity on my name tag so i can meet people easier. (I am shy!)
A side effect is that when people learn about my alter-ego, many start telling me about all the trouble they are making with parametric families.
One fellow, Mr. Kelvin Tam of NBBJ, was ecstatic to meet me because he had been working on a parametric soccer ball and somehow knew that i would appreciate it.

Well actually Kelvin, I am an NFL guy and I HATE soccer...but i do appreciate monkey business on this scale!

His email started with this explanation of  Platonic Solids

http://en.wikipedia.org/wiki/Platonic_solid

Which is a discussion that wnet completely over my head.

Then i got into the meat of the matter.  Picked one of the patches and opened it up

Ok.  Looks like a disc thats cut by some voids.

But when you look at the dimensioning that going on, thats where i was impressed...because it had to be programmed so that not all sides were equal.  I especially like the dimension that controls the radius of the sphere that trails off into space.

Here is the parameters for this patch:

Pretty straight-forward.  Then i took a look at the faces all these families are hosted on.  Whoa! Whoa! Whoa! Whoa! Stop The Clock!

And then the parameter stack that is controlling this mess in the host family:

Anyone who ends a formula with 4 closed parenthesis is okay by me.  Kelvin, I have no idea how you did all this, but i am very sure you care alot.  I salute your passion!

You can find the family for download here:

Soccer Ball.rfa
(I replaced original file with a ZIP file so it should work now)