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MathGroup Archive 1999

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Q: meaning of 'order n' of a regular tessellation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16097] Q: meaning of 'order n' of a regular tessellation?
  • From: wacb at aplcomm.jhuapl.edu (Bill Christens-Barry)
  • Date: Thu, 25 Feb 1999 08:24:56 -0500
  • Organization: Johns Hopkins University Applied Physics Laboratory
  • Sender: owner-wri-mathgroup at wolfram.com

The Mathematica documentation, online help, and Wolfram's support URL at

http://www.wolfram.com/support/2.2/Kernel/Symbols/Graphics/Polyhedra/Geodesate.html

all explain the Geodesate[epxr, n] command (from the Graphics`Polyhedra`
package) with the following:

Geodesate[expr, n] replaces each polygon in expr by the projection onto
the circumscribed sphere of the order n regular tessellation of that
polygon. Geodesate[expr, n, {x, y, z}, radius] does the projection onto
the sphere of size radius centered at {x, y, z}.

Where can I get an explanation of the meaning of the term 'order n'
regular tessellation of a polygon. In particular, I am finding that
increasing the order n of the tessellation does not cause the edge lengths
of the triangles created to decrease as rapidly as I hoped to see, and I
would like to understand why. If you have specific literature references,
please pass them along.

My goal is to subdivide the surface of the unit sphere into as regular a
set of small subregions (triangles) as possible. I would like the
variances of the sizes and the edge lengths of these subareas to be as
small as possible. In particular, I would like the edge lengths of these
regions to subtend no more than 1 degree. Please suggest any alternative
procedures that I might use.

Thanks.

Bill Christens-Barry


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