Take the plane of one face of an icosahedron and intersect it with all
the other planes. Use the resulting lines to divide this plane into 67
sectors. "Fill in" certain combinations of these sectors and use them as
one face on the icosahedron, then copy it and rotate it into place for
the other faces. (There are 59 such combinations, this is only a select
few.)
The trig should only take you all day, but then again, you enjoyed it,
you're a flaming math nerd, aren't you? :-)
--
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"Sitting on a cornflake, waiting for the van to come" -Beatles
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