 The geodesic distance between two points x and y on the unit sphere S^{2} is
dist(x,y) = cos^{1}(x^{T} y).
 The sphere packing problem is to place m points on a sphere to as to maximize the
the minimal distance, or minimal separation, between them.
 For maximum determinant systems the minimum distance between points is known to be asymptotially greater than π/(2n).
Numerically the minimum angle is closer to π/n.
 Mesh norm is
h = max_{x in S2} min_{j=1,...,dn} dist(x, x_{j}).
This is also the covering radius for covering the sphere by spherical caps.
 Potential energy (Riesz s = 1 energy) is sum over all distinct points x_{i} and x_{j} of
1 / x_{i}  x_{j}_{2}
 Cui and Freeden discrepancy is
D =
(1/(2 d_{n} sqrt(π)))
[ sum_{j=1,...,dn} sum_{k=1,...,dn}
(1  2 log(1 + sqrt((1  x_{j}^{T} x_{k})/2)) ]^{1/2}.
 Volume of the convex hull of a set of points on S^{2} is always less than the volume of the unit sphere
= 4 π / 3 = 4.18879...
 The Voronoi cell V_{j} for point x_{j}, j = 1,...,d_{n} is
V_{j} = {x ∈ S^{2} : dist(x, x_{j}) ≤ dist(x, x_{i}), i ≠ j}
 If there are only pentagonal (5 sides), hexagonal (6 sides) and heptagonal (7 sides) Voronoi cells
then Euler's formuula implies the number of pentagons is equal to the number of heptagons + 12.

