[math-fun] Projection of a dodecahedron onto an unrolled cylinder
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
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
Yes, that's the thing. I would like to see the result with the cylinder unrolled into a 1-by-pi rectangle. 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
Straight lines project to piece of sinusoids, right? On Tue, Feb 4, 2014 at 5:49 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
Yes, that's the thing. I would like to see the result with the cylinder unrolled into a 1-by-pi rectangle.
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
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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
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
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
Thank you, Neil. I think that Wikipedia may have what you are describing on their dodecahedron page (that page is marvelous, by the way). Alan, 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
participants (4)
-
Allan Wechsler -
Henry Baker -
Hilarie Orman -
Neil Sloane