On Wed, Oct 1, 2014 at 7:04 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Very interesting question. (Are you requiring that all intersections between great circles be nodes? Or are extraneous intersections allowed?)
I'd prefer to have just the proper intersections, if possible.
Let tau = exp(2pi*i/6). There's a highly symmetrical version of the Fano plane on the torus T = C/L, where C = complexes and L = Z[2+tau].
Let S = {0, tau^k | 0 <= k < 6} and draw a circle of radius sqrt(1/3) about each z in the image of S in T = C/L.
These 7 circles each intersect 3 others, for a total of 7 intersection points in T.
The incidence relations among these 7 circles and 7 intersection points is isomorphic to the Fano plane.
Interesting!
(Which leaves Mike's question unanswered, alas.)
--Dan
On Oct 1, 2014, at 2:47 PM, Mike Stay <metaweta@gmail.com> wrote:
. . . can you assign each point in the Fano plane to antipodal points on the sphere and each line in the Fano plane to a great circle such that the incidence relation is preserved?
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