a MUCH better photo of the icosahedron

[franktaw at netscape.net]

I  haven't seen Bien's paper, but I strongly suspect that it is an 
example of
what might be called the "Dr. Matrix effect": if you look hard enough 
for
patterns of a particular type, you will find them.

I can't say exactly why the craftsman chose the numbers he did 
(especially
the 20 and 202), but it seems clear to me that it is just a numbering
scheme, with no deeper meaning.

Franklin T. Adams-Watters

(For those too young to remember - Dr. Matrix was a fictional character 
in
Martin Gardner's Mathematical Games columns in Scientific American - 
which
nurtured the interests of many of us in mathematics.  Dr. Matrix was a
numerologist/con man, who specialized in obscure numerological links to
whatever his current scam was.)

-----Original Message-----
From: ron at ronknott.com

Paul Bien wrote a paper on this numbered icoshedron, presented at the
10th Conference on Fibonacci Numbers and their Applications (2002) but
which did not appear in the Proceedings. It appeared in an earlier
format in The Eighth Midwest History of Mathematics Comference, October
2000.

       / \  / \
      /202\/601\
      -----------
      \901/\701/
       \ /801\/
 ---------------------
\ 11/\91/\ 71/\ 51/\ 31/\
 \ /20\/ 81\/61\/ 41\ /21\
  ------------------------
  \101/\201/\301/\401/\501/
   \/   \/   \/   \/   \/

The hinge is on the edge common to the faces 71 and 801 witht he top
section as shown here being on the lid.  He relates the sums of numbers
in thetop, round the middle bottom and total to give approximations (to
3 dps)  to Pi, Pi squared, Pi cubed, Phi (golden mean), Phi squared,Phi
cubed,  root 2, root 3 and root 6


Ron Knott



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