From: jcarney@mit.edu (John C. Carney) Newsgroups: sci.math Subject: HOW? Equally spaced points on a sphere?? Date: 20 Jan 1995 23:05:48 GMT This question is bugging me (I am not a math person). How do I uniformly space points on a sphere? I have a ball and I'd like to put X points uniformly spaced on the surface of it. The number X is not very important (I want it to be about 40 to 80). Is there some way using a compass and ruler that I can accomplish this? What do I mean by uniformly spaced? Say I put 50 electrons on a metal sphere. What is one solution to where these points will distribute themselves? Thank you very much! John Carney, Massachusetts Institute of Technology jcarney@mit.edu ============================================================================== From: fritz@rodin.wustl.edu (Fritz Lehmann) Newsgroups: sci.math Subject: Re: HOW? Equally spaced points on a sphere?? Date: 21 Jan 1995 04:12:58 GMT In article <3fpfkc$mgf@senator-bedfellow.mit.edu>, John C. Carney wrote: >How do I uniformly space points on a sphere? I have a ball and I'd like >to put X points uniformly spaced on the surface of it. The number X is >not very important (I want it to be about 40 to 80). Is there some way >using a compass and ruler that I can accomplish this? >What do I mean by uniformly spaced? Say I put 50 electrons on a metal >sphere. What is one solution to where these points will distribute >themselves? >John Carney, Massachusetts Institute of Technology >jcarney@mit.edu If I understand you correctly, you will be unable to put 40, 50 or 80 points on a sphere at all, if they are to be "uniformly spaced". "Uniformly spaced" points necessarily form a regular (Platonic) polyhedron. So you can uniformly space 0,1,2,4,6,8,12,20 and infinity points on a sphere, and no other number. (The infinity is a little controversial, though.) Your statement that "The number X is not very important" is not consistent with all this, so maybe you meant something by "uniformly spaced" other than what I thought you meant. Yours truly, Fritz Lehmann ============================================================================== From: Laura Helen Newsgroups: sci.math Subject: Re: HOW? Equally spaced points on a sphere?? Date: Sat, 21 Jan 95 14:37:15 -0500 This really should be in the FAQ. I got this from a mailing list: Laura from N J A Sloane Announcement: Tables of Points on Spheres The main tables are of packings (with N <= 130, d = 3,4,5), but there are also tables of coverings, minimal-potential arrangements, arrangements which maximize the volume of the convex hull, packings with icosahedral symmetry, all on the sphere. There are also tables of minimal-energy clusters of N spheres in d-space, and clusters which attempt to minimize the Lennard-Jones potential. Much of this material will be published in a book ("Spherical Codes", in preparation), but in view of the considerable recent interest in these problems, both on the net and in journals, we are making these tables available before the book is completed. The tables are in netlib, and can be accessed by e-mail, ftp or mosaic: 1. By e-mail: to see what is available, send messages like send index from att/math/sloane (or from att/math/sloane/packings, or att/math/sloane/packings/dim3, etc.) to netlib@research.att.com. To obtain one of these codes, send a message such as send att/math/sloane/packings/dim3/pack.3.92 to netlib@research.att.com. 2. By ftp: connect by ftp to netlib.att.com, login as anonymous, use your e-mail address as password. Type binary cd netlib/att/math/sloane You can then use "ls" to see what files are available, "get" to fetch them, "cd" to move to subdirectories, etc., and "quit" to quit. 3. From a mosaic document viewer, you can get directly to the material. Open an URL address such as: ftp://netlib.att.com/netlib/att/math/sloane/index.html.Z ftp://netlib.att.com/netlib/att/math/sloane/packings/index.html.Z ftp://netlib.att.com/netlib/att/math/sloane/packings/dim3/index.html.Z This will give you a screen of short descriptions of all the items available. Clicking on one gives you the document, which can then be saved in a file. We would appreciate hearing of any improvements to these tables; all such improvements will be credited in the tables. Send them to either of the first two authors. N. J. A. Sloane (njas@research.att.com) R. H. Hardin (rhh@research.att.com) Math. Research Center, Room 2C-376, ATT Bell Labs, Murray Hill NJ 07974 USA Warren D. Smith (wds@research.nj.nec.com) NEC Research Corp., Princeton NJ USA