[r-t] Rotations of a truncated icosahedron

Alexander Holroyd holroyd at math.ubc.ca
Wed Nov 17 00:50:24 UTC 2004

Very interesting, PABS.  Do you have a simple formula for the coordinates
of your vertices?

My pictures come from a different approach.  Let (a,b,c,d,e) be the
_inverse_ of a given row (so bell 1 is in place a, bell 2 is in place b
etc.).  Then I put the vertex correponding to this row at 3d coordinates:
 a+b-c-d   a-b+c-d   a-b-c+d
(------- , ------- , -------)
   K-e       K-e       K-e
where K = 3 + 2 Sqrt(2) = 5.828

I'll explain why shortly - the construction extends in principle to any
number of bells.  I'll also make some more pictures soon.  By the way, the
3d graphics were produced by:


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