From pbeck@pica.army.mil Tue May 21 11:10:45 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA22456; Tue, 21 May 91 11:10:45 EDT Date: Tue, 21 May 91 11:03:02 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: bilinski rhombicdodecahedron Message-Id: <9105211103.aa16846@FSAC1.PICA.ARMY.MIL> 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