> Yes!  If you have an icosahedron with edge lengths of one, you can
> inscribe three mutually orthogonal golden rectangles.  With the
> dodecahedron, you can inscribe three mutually orthogonal rectangles in
> the ratio phi^2 (which incidentally is phi + 1).
> 

I looked at my paper models of the icosahedron and the dodecahedron and
saw the rectangles.  This should help with finding the coordinates of
the vertexes.  It's almost magic.  Thank you!  :-)

The golden ratio is one of those mysterious irrational numbers.  As you
said, its square is equal to the sum of one and itself.  Its reciproial
is equal to its value minus one.  I wonder if there's an undiscovered
equation that relates it to other constants like e^(i*pi) + 1 = 0.

I have seen the number called the golden mean.  It is because a golden
rectangle has a mean ratio between its sides and not extreme ones?
Brendan

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