[next] [prev] [up] Date: Tue, 21 May 91 11:03:02 -0400 (EDT)
[next] [prev] [up] From: Peter Beck <pbeck@pica.army.mil >
~~~ ~~~ [up] Subject: bilinski rhombicdodecahedron

I would like help on finding info on the "BILINSKI" rhombic

BACKGROUND: The common rhombic dodecahedron is the KEPLER and its
diagonals are in the ratio of 1:sqr rt of 2. The Bilinski has its
diagonals in the ratio of 1:tau (ie, the golden section ~ 1.618).
The only reference I have been able to find so far is on page 31 of
Coxeter's "Regular Polytopes".

.. Is there a proof of why there are only 2 rhombic dodecahedrons?
.. are there any interesting features of how the Bilinski fills
space? Any interesting relationships with other polygons, eg,
.. Has anybody studied the dissections of the bilinski? Is there any
significance that it takes both obtuse and acute rhomboids to
construct a bilinski while a kepler only requires an obtuse?
.. Is there a crystal or some other real world object that
corresponds to the bilinski?
.. Any ideas on fixturing/jigging to make bilinski's from wood?

Thanks for any help.
Pete Beck <pbeck@pica.army.mil>

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