Hilarie> Thank you, Neil. I think that Wikipedia may have what you are describing on their dodecahedron page (that page is marvelous, by the way). < Except that it still uses http://en.wikipedia.org/wiki/File:Pyritohedron_animation.gif instead of http://gosper.org/pyrominia.gif, and doesn't discuss the endododecahedron, nor Julian's equilateral, topologically regular one. Hilarie> Al[l]an, yes, I believe that dodecahedron edges project to pieces of sinusoids. The projection looks something like two lines of clenched teeth, 5 up, 5 down, with scalloped edges on the top and bottom. Hilarie Date: Tue, 4 Feb 2014 18:32:08 -0500 From: Neil Sloane <njasloane@gmail.com> Hilarie, This is not an answer to your question. But it might be helpful to start with nice coordinates. Let t = golden ratio (1+sqrt 5)/2. Then the 8 points (+-1, +-1, +-1) together with all twelve cyclic shifts of (0, +-1/t, +-t) form a dodecahedron (they lie on the sphere of radius sqrt 3). Given the points, you can do anything you want. Page 157 of my notebook Latt 22 has a sketch with lots more data - I could send you a pdf of a scan if you want. But that's a long way from an svg file of course Neil On Tue, Feb 4, 2014 at 6:05 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
What I really want is the projection of a dodecahedron onto a sphere, and that projection projected onto a cylinder (hat-box style), and that projection unrolled into a rectangle. As an svg file.
Hilarie
Date: Tue, 04 Feb 2014 02:52:37 -0800 From: Henry Baker <hbaker1@pipeline.com> Do you mean a projection of the Archimedes "Hat Box Theorem" type?
At 12:55 AM 2/4/2014, Hilarie Orman wrote:
I'm looking for a diagram of a dodecahedron projected onto a 1x1 cylinder. svg file would be delightful.
Google is perversely biased towards projections of the earth onto dodecahedra.
Hilarie
--rwg When my brainscan didn't show anything it was like a great weight lifted from my shoulders.