Re: tessalation of a sphere
- To: mathgroup at smc.vnet.net
- Subject: [mg9283] Re: tessalation of a sphere
- From: weber at math.uni-bonn.de (Matthias Weber)
- Date: Mon, 27 Oct 1997 02:46:54 -0500
- Organization: RHRZ - University of Bonn (Germany)
- Sender: owner-wri-mathgroup at wolfram.com
In article <62pedv$acs at smc.vnet.net>, "I. Inanc Tarhan" <tarhan at piranha.cis.upenn.edu> wrote: > Hi all, > > Would anybody have information on, or pointers to the subject of > representing a sphere as a number of equidistantly spaced points on its > surface (i.e., if you can fold open the sphere without any distortions, > the points will be hexagonally "close" packed)? Specifically, I am > trying to represent the surface of a sphere as a collection of > identical equilateral triangles. > > Any good ways of doing this with Mathematice? > There is a much more general theorem of Aleksandoff stating that this is possible if there are at most 6 triangles around each vertex as the boundary of a convex body in R^3. Hence if you actually want to do it with a given combinatorial triangulation, this problem reduces to solving a bunch of linear equations, which Mathematica should be able to do. I don´t know about ready code doing this. A general reference for your problem are Voronoi diagrams. There is a vast literature about them, just search the net. Matthias Weber