How did those guys at Geomag come up with the new bar length? Here's one possibility - first let's
take some careful measurements:
So, the geometric length turns out to be: 69.94mm
Now, a double-length Geomag original bar has geometric length: 65.78mm
and the ratio between these two numbers is: 0.94 - remember that!
Look in wikipedia to get the circumradius of the icosahedron
http://en.wikipedia.org/wiki/Icosahedron
it's 1/4sqrt(10+2*sqrt(5)) = 0.95106
Coincidence? maybe.
Some calculations give away that a double-length Geomag classic rod is
just 0.74mm short of the required length to act as the radius element
for a starburst icosahedron. And 0.8mm is 1/32" which is just the size of
some little magnetic shims I happen to have handy.
Here's a detail of 12 rods arranged around a ball with icosahedral symmetry.
Should you wish to try this at home, you can manufacture shims easily by
using a hole-punch on one of those magnetic stickers you probably have on the fridge: the
disks ejected by the hole punch are just the right size for Geomag bars.
Here's an example: http://www.flickr.com/photos/karlhorton/404972512/in/set-72157594564548492/