Won't they struggle a little with Thurston geometrisation etc? WFL On 3/11/14, Hilarie Orman <ho@alum.mit.edu> wrote:
Stuart, thanks, that's almost exactly the dodecahedron I was looking for!
I've forwarded a copy of the paper to my city's planning commission.
Hilarie
Date: Tue, 11 Mar 2014 19:21:27 +1100 From: Stuart Anderson <stuart.errol.anderson@gmail.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Projections -> sphere <-> rectangle
There is another way to go from a dodecahedron to a rectangle. It's not a projection but a combinatorial mapping with software by J. W. Cannon, W. J. Floyd, and W. R. Parry. http://www.math.vt.edu/people/floyd/research/software/subdiv.html (see bottom of the page for the dodecahedron data) The first program subdivide.c prompts you for a subdivision rules file and a tiling file for a quadrilateral, and returns the tiling file for the subdivision. Once you have the tiling file you can convert it with a second program tilepack.c to use with Ken Stephenson's circle packing program, CirclePack http://www.math.utk.edu/~kens/CirclePack/, to draw the tiling to be Euclidean or hyperbolic. Alternatively you can use the third program squarect.c to create a squared rectangle from the dodecahedron.
see http://www.math.vt.edu/people/floyd/research/papers/fsr.pdf for more
Stuart Anderson