Re:Evenly distributing points on a sphere
by mabbo on Saturday August 25, 2018 @06:26PM
(#17842918)
Your post shows values of d=2, 3.09, 3.29 and 3.31 with different latices. There must be some theoretical maximum d possible, right? Some upper bound that "d cannot be greater than X"? What do we know about the bounds of that maximum value?
[ Parent
| on HN ]
Re:Evenly distributing points on a sphere
by extremelearning on Saturday August 25, 2018 @06:42PM
(#17842979)
The values for the tetrahedron, cube, octahedron, dodecahedron and icosahedron are:3.27, 3.27, 3.46,3.19 and 3.64, resp.
These produce the largest d for N=4,8,6,12 and 20 resp. Thus, it is presumed by almost everyone that d=3.64 is the global upper bound.
Unfortunately, I believe it is still an open problem to to prove this or to describe a general upper bound for specific N not equal to any of these five values.