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