From: jbuddenh@artsci.wustl.edu (Jim Buddenhagen)
Newsgroups: sci.math
Subject: Re: Rhombohedrons
Date: 31 Oct 1995 01:14:11 GMT

[all deleted]

The rhombic dodecahedron is also a space filler:  attach equal cubes to the
six faces of a cube.  The rhombic dodecahedron has for its vertices the
eight corners of the original cube and the centers of the attached cubes.
e.g.  (+-1,+-1,+-1), (+-2,0,0), (0,+-2,0), (0,0,+-2).   

The rhombs have the edges of the original cube for their short diagonals
and edges of the dual octahedron for their long diagonals.  The long
diagonals join centers of the cubes which were attached to adjacent faces
of the original cube.  The diagonals are thus in the ratio 1:sqrt(2).

--Jim Buddenhagen (jbuddenh@artsci.wustl.edu)