From: teichman@slinky.cs.nyu.edu (Marek Teichmann)
Newsgroups: sci.math
Subject: Distributing points "evenly" on a sphere
Date: 27 Aug 1995 21:57:05 -0400

Hello,
I am looking for a result of the following type:

  Place N points on a unit sphere in R^3, so that the largest sphere
  concentric with the first, and inscribed in the convex hull
  of the points, is as large as possible.
  What is a lower bound on the radius of the inscribed sphere given N?

In other words, if the sphere is centered at the origin, we wish
to maximize the distance from the origin to the closest facet of the
convex hull of the points.

A result of this type exists for large N in arbitrary dimension,
but for three dimensions, the result starts applying for about N > 60000.
( the reference is D.Kirkpatrick, B.Mishra, and C.-K. Yap,
Quantitative Steinitz's theorems with applications to multifingered grasping.
Discrete Comput. Geom., 7:295--318, 1992.)

Thanks in advance for any ideas/references,
	Marek
	teichman@cs.nyu.edu