I think this is just gorgeous. Is Fred's solution the unique* set of points in R^3 having the combinatorial type of the Fano plane (with unit circles for the lines) and the symmetry group of D_3 == S_3 ??? —Dan _____________________________________ * Up to isometries of R^3, of course.
On Jun 30, 2015, at 11:12 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Two views of FWH solid circular Fano plane at https://www.dropbox.com/s/iofsjqyln0n929d/hele_solid0.gif?dl=0 https://www.dropbox.com/s/zs7pi91p0f99m5o/hele_solid1.gif?dl=0 the first showing 6-fold symmetry about z-axis, the second with z-axis up page showing one (of 3) adventitous double point below right of centre.
No coordinate box this time. For nothing is simple. FWH's circle #1, parallel to xy-plane with centre on z-axis, defeated all attempts to plot it until in desperation I rotated everything thru' an entire radian around all three axes ... Maple solve() moves --- or in this case, fails to go anywhere --- in mysterious ways!