Dylan Thurston wrote:
..."A Color-Matching Dissection of the Rhombic Enneacontahedron"...
Any chance of a version that is not in .doc format (e.g., PostScript)?
I just put an html version at: http://www.georgehart.com/dissect-re/dissect-re.htm
On trying to count efficiently: I wonder if it's possible to apply your technique of picking an equatorial band repeatedly, picking, say, two different directions and looking at all the possibilities for the two cases. Of course the two will interact, but maybe it's possible to control that.
I don't see how to work out the details of this.
On the other hand, isn't it possible to think of a decomposition of a 3-d zonotope into parallelipipeds as a sequence of decompositions of a 2-d zonotope into parallelograms? I guess that's what this paper:
http://www.liafa.jussieu.fr/~latapy/Publis/Pav/abstract http://www.liafa.jussieu.fr/~latapy/Publis/Pav/Pav.ps.gz
Latapy didn't realize when he wrote his papers that the combinatorial form of the zonotope affects the answer. For example there are four combinatorially distinct 6-zone zonohedra, including a polar zonohedron (which has two vertices of order 6) and Kepler's rhombic triacontahedron (which doesn't). The number of dissections is different for these but Latapy assumed it only depended on the number of zones. Thus his entries in the EIS are incorrect/incomplete. I corresponded with him a year ago about this. He said:
Actually, I do not work on these topics anymore.
You might want to go back and clarify the information in Sloan's database. I certainly have to ! I'll try to do this soon.
George http://www.georgehart.com/