Quote:
Originally Posted by ccorn
Here is it:
(+/r^{1}, +/r, 0) (permute cyclicly), (+/1,+/1,+/1) dodecahedron
(I have used r = (1+sqrt(5))/2, hence 1/r = r1, but the above scheme can be used with r's conjugate as well.)

Sounds right to me.
The edges of one are perpendicular to those of the dual.
I've just remembered why I brought this up:
World cup football!
In Mexico 1970 they first used a truncated icosohedron,
(20 white hexagons and 12 black pentagons).
Better known these days as C60 or Buckminsterfullerine.
I can't see why he found it so difficult to think of
a structure with 60 vertices.
I made one out of cardboard at the time, also
the great(?) stellated(?) dodecahedron which
makes a beautiful Christmas decoration.
David