[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:
http://wwwvis.informatik.uni-stuttgart.de/~kraus/LiveGraphics3D/
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