I found (most of) the answer to my question by reading Clinton's Equal Angle Conjecture a bit more carefully-

See:

http://www.freewebtown.com/randome/ClintonEqualEdge.pdf

"Clinton's Equal-Angle Conjecture" proposes: "A sphere may be tessellated in such a manner that it will be made up of a group of spherical polygons, with edges having equal central angles and having the topological characteristics of the Goldberg polyhedra."

If one wants to make a spherical grid of equal edge hexagons and pentagons, how would one calculate what strut lengths will produce what diameter spheres? If the "conjecture" is true, then there will be many lengths which would work for any given diameter.

For a simple example, a dodecahedron consists of 12 pentagons with all equal edge lengths, and the vertices lie on the surface of a sphere. A buckyball, consisting of 12 pentagons plus 20 (I think) hexagons all of which have the same edge length can also be inscribed in the same diameter sphere. The individual edge lengths in the buckyball are of course shorter than the edges of the dodeca, if they both define the same size sphere.

According to Clinton's conjecture (which I have reason to believe is true!) there is a whole family of spherical hex/pent grids with a single edge length which could be inscribed in the same diameter sphere. Only specific edge length/subdivision combinations will work for any specific diameter, but any number of finer and finer subdivisions, using a single length, can form a sphere of a given diameter.

Does anyone know how to calculate the ratio between these lengths and the diameter of the sphere?
(Or perhaps a handly set of chord factors?)

Bob Sanderson

hi phil

if you look up chris fearnley's web site he keeps track of the collaroborative meetings that have happened let say like the last two years in at SUNY owego new york. or get a hold of john belt who teaches in at OSWEGO as you know there are a lot of takes on physics form sting theory on down the line in the beyond

I have heard that synergetics can model the strange behavior demonstrated in quantum physics. I would like to find any existing research that has been done to explore this apparent similarity. If no one knows of any such research, I would also appreceate any advice on how to get started.