Math for a geodesic sphere

Question

I\'m trying to create a very specific geodesic tessellation, but I can\'t find anything online about it.

It is normal to subdivide the triangles of an icosahedron in

Answer 1

Marcelo,

The most-commonly employed geodesic tessellations are either Class-I or Class-II. The image you reference is of a Class-III tessellation, more-specifically, 4v{3,1}. The classes can be diagrammed, so:

Class-III tessellations are chiral, and can have left-handed or right-handed twist. Here's the mirror-image of the sample you referenced:

You can find some 3D models of Class-III spheres, at Google's 3D Warehouse: http://sketchup.google.com/3dwarehouse/cldetails?mid=b926c2713e303860a99d92cd8fe533cd

Being properly identified should get you off to a good start.

Feel free to stop by the Geodesic Help Group; http://groups.google.com/group/GeodesicHelp?hl=en

TaffGoch

Answer 2

I believe it is actually just a matter of resolution (i.e., number of sub-divisions). The tessellation you show does seem to emanate from an icosahedron scheme: cf p.7 here, mid-page example. Check out the rest of the document for some calculation details - also its cited references, and some further code samples here.

Answer 3

Marcelo,

If you want to devise algorithms to generate any class of geodesic spheres, you can do it here:

http://thomson.phy.syr.edu/thomsonapplet.htm

Start by using the "custom(m,n)" option, select your desired parameters, then hit the "pause" button. Switch to "lattice energy" and hit the "Auto" button.

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If you're intimately familiar with java, you can save the "jar" file(s) for this app, and examine the contents, to back-engineer the algorithms.

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BTW, this java app also has a "File" menu option, which can activate a new window, listing the "Point set" (vertex coordinates.) I copy & paste them into an Excel spreadsheet, from which I can generate a "csv" file that can be, subsequently, imported into 3D-graphic programs.

Taff

Answer 4

Here's an image from one of Joe Clinton's NASA publications: