From:

~~~ ~~~ Subject:

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

dodecahedron.

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".

AREAS OF INTEREST

.. 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,

triacontahedron?

.. 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>