Geodesic Grids Wikibook

[Apocheir V]

Hello, everyone.

I've been working on a book at Wikibooks on the topic of geodesic grids. I've just recently completed the bare-bones beginnings, so I figured now was a good time to share it. You can view it here: http://en.wikibooks.org/wiki/Geodesic_Grids

This was born of my frustration that there wasn't a complete resource already in existence. Yes, there's Domebook and Geodesic Math and How to Use It and Clinton's papers, but most of them only covered Class I and II on the icosahedron, barely mentioning the other options. I think the book contains some new information; for instance, I've never seen anyone do Method 2 for a Class III grid before, and I introduce a couple variations on Method 1 that I think may be new. Then again, I'm missing a few of the existing methods.

I am relatively new to the study of geodesic domes & grids, so I'd appreciate any comments you have; terms I'm using incorrectly, things I think are innovations that really aren't, etc. It's a wiki, so feel free to jump in and add your knowledge.  

Thank you!

[Adrian Rossiter]

Hi Apocheir

On Wed, 29 Apr 2015, Apocheir V wrote:
> I've been working on a book at Wikibooks on the topic of geodesic grids.
> I've just recently completed the bare-bones beginnings, so I figured now
> was a good time to share it. You can view it here:
> http://en.wikibooks.org/wiki/Geodesic_Grids

Looks good. Well done.

> on the icosahedron, barely mentioning the other options. I think the book
> contains some new information; for instance, I've never seen anyone do
> Method 2 for a Class III grid before,

I use Method 2 with Class III models, following a description by
Joseph Clinton, but I am not sure in which paper.

http://packinon.sourceforge.net/py_progs/pg_geo.html
http://www.antiprism.com/programs/geodesic.html
http://www.antiprism.com/examples/200_programs/650_geodesic/imagelist.html
http://www.antiprism.com/examples/150_named_models/570_geodesic/index.html

Regarding faces and edges, a convex hull will work in a lot of
spherical cases, but fails for tetrahedral models fairly soon as
the frequency increases. As I wanted a solution that worked with
arbitrary polyhedra I came up with a purely combinatorial
algorithm for determining the faces. The following commands
show this woking for a tiling of a torus, which is converted to
a 2,1 geodesic pattern (images attached).

unitile2d -s t 10 -w 10 -l 30 | off_color -f N | antiview -t no_tri
unitile2d -s t 10 -w 10 -l 30 | off_color -f N | geodesic -c 1,2 -M p | antiview -E white -v 0.01

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

[Gerry in Quebec]

Hello Apocheir,

A fairly recent source that will surely interest you, if you haven't already seen it, is Edward S. Popko's book, Divided Spheres: Geodesics & the Orderly Subdivision of the Sphere. This is major work that may end up becoming the "bible" of geodesic geometry. Published in July 2012, it covers a range of geodesic topics and subdivision methods and devotes pages 231-244 to class III structures (the full hardcover book is 535 pages).

You mentioned the question of terminology.... Popko's illustrated glossary runs from page 453 to 478. He also has a huge bibliography, from page 481 to 500.

Here are some links:
 
https://www.crcpress.com/product/isbn/9781466504295

http://www.amazon.ca/Divided-Spheres-Geodesics-Orderly-Subdivision/dp/1466504293

http://www.amazon.ca/Divided-Spheres-Geodesics-Orderly-Subdivision/dp/1466504293

I'll check out your work on the Wikibook. Thanks.
 

- Gerry in Quebec

[Gerry in Quebec]

Here's the 3rd Popko-related link I meant to post earlier:

http://www.dividedspheres.com/

- Gerry