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The starburst icosahedron with long bars

PostPosted: Sun Dec 27, 2009 2:13 am
by karlhorton
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
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: