This does not answer your question, but I find it pretty interesting.
In "Telescope mirror supports: plate deflections on point supports" by Jerry Nelson, Jacob Lubliner, and Terry Mast (the designers of the Keck mirror support system from UC Berkeley) SPIE Vol. 332, 1982, they consider the case where deflection that changes the focal length IS significant, as it would be for any telescope with a segmented mirror, an optical flat, or for diffraction limited long exposure work. They also assume, as everyone else does, that the mirror is of uniform thickness. So these results will not be exactly right for mirrors ground from flat blanks. They state in terms of RMS deflection:
"The three point support is the most common of support systems, and its optimum occurs at the well known radius of beta = 0.645..."
Their results also show that three points at the edge, beta = 1.0, is about four times worse (RMS) than at beta = 0.645. Optimum for six points is a hexagon of radius 0.683 which has about half the RMS deflection of a three point system. And they show many more complex designs with lots of points.
Chuck