From: "Thane Plambeck" To: "Alan Schoen" Subject: Re: reoriented cube compound Date: Thursday, May 15, 2003 12:00 PM I've spent some more time investigating the non-constructability of the 3 cube twice-twisted model in Zometool. After reading this page of George Hart's http://www.georgehart.com/virtual-polyhedra/zometool.html , (especially what he has to say with about the cube)... I realized that the difficulty is closely related to the fact that the Zometool cube doesn't have all the symmetries of a cube, instead, it has tetrahedral symmetry, as George describes. (The sides are all of the same length, and the angles are all 90 degrees, but the fully assembled object, including the zome vertices, has only the symmetry of a tetrahedron). In fact, not even all possible orientations of one rotated cube within another are realizable, which I hadn't noticed until just now; ie, fixing the body diagonal, there's only one way to do the rotation. I haven't made changes to the web page with your new diagrams, but plan to. Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm