Model of PG(3.2)

A model of the smallest projective space, PG_3(2) in dimension 3 over the field with 2 elements.
This space consists of 2^3+2^2+2^1+2^0=15 points and 35 lines (All edges and circles are to be interpreted as lines). A more thorough description can be found at:
http://en.wikipedia.org/wiki/Finite_geometry

This structure for example can be used to find a solution for Kirkman's schoolgirl problem: http://en.wikipedia.org/wiki/Kirkman%27s_schoolgirl_problem