a related but more interesting/flexible question is: what is the maximum volume of the convex hull of N points on a unit sphere in D dimensions? Also of interest, same question, but "hyperbolic volume" not euclidean volume. That is the interior of the unit sphere in D-dimensions, can be regarded as hyperbolic D-space (nonEuclidean geometry) there is such a a model where straight Euclidean lines correspond to hyperbolic geodesics. Also, the Poincare disk model has hyperbolic geodesics corresponding to Euclidean circular arcs (perpendicular to the unit sphere where touch it) in which case the "convex hull" faces are no longer pieces of euclidean hyperplanes but rather euclidean sphere pieces. Of course, the maxvol configurations are non-unique via rotation, but the hyperbolic maxvol configurations have an even larger nonuniqueness than that, because any isometry of hyperbolic space can be used, which includes "boosts" (the hyperbolic analogue of a translation) as well as "rotations."