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Re: equally spaced points on a hypersphere? [message #41542 is a reply to message #41449]

Fri, 29 October 2004 08:53

Matt Feinstein
Messages: 33
Registered: July 2002

Member

On 29 Oct 2004 10:29:31 -0500, Craig Markwardt
<craigmnet@REMOVEcow.physics.wisc.edu> wrote:

> So is there any requirement that the tesselation produce a regular
> polyhedron?
>
> Clearly it is possible to place *any* number of equidistant points on
> a sphere via an iterative approach. As discussed on line, start
> with random placement of points, allow the points to repel each other,
> iterate until you reach the lowest energy configure.
>

I think that if 'equidistant' means that each point has the same
relation to -every- neighboring point, then it implies that the points
lie on a regular polyhedron. In any case, a lowest energy
configuration may only be a local minimum with respect to small
variations of the positions of the points, so the global properties of
such a minimum are not necessarily unique.

Matt Feinstein

--
There is no virtue in believing something that can be proved to be true.

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[Message index]

		equally spaced points on a hypersphere? By: robert.dimeo on Fri, 29 October 2004 07:51
		Re: equally spaced points on a hypersphere? By: robert.dimeo on Mon, 01 November 2004 05:34
		Re: equally spaced points on a hypersphere? By: jeyadev on Fri, 29 October 2004 11:00
		Re: equally spaced points on a hypersphere? By: James Kuyper on Fri, 29 October 2004 10:18
		Re: equally spaced points on a hypersphere? By: James Kuyper on Fri, 29 October 2004 10:24
		Re: equally spaced points on a hypersphere? By: James Kuyper on Fri, 29 October 2004 09:52
		Re: equally spaced points on a hypersphere? By: Craig Markwardt on Fri, 29 October 2004 09:40
		Re: equally spaced points on a hypersphere? By: tam on Fri, 29 October 2004 09:10
		Re: equally spaced points on a hypersphere? By: Matt Feinstein on Fri, 29 October 2004 08:53
		Re: equally spaced points on a hypersphere? By: Craig Markwardt on Fri, 29 October 2004 08:29
		Re: equally spaced points on a hypersphere? By: Matt Feinstein on Fri, 29 October 2004 08:16

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