A Finite Geometry Exercise 1.5.
Where there is matter, there is geometry.
—Johannes Kepler (1571–1630)

Exercise 1.5. Show the two models for Fano's geometry are isomorphic.

Set up a 1-1 correspondence between the points and lines by assigning A to 1, B to 3, C to 5, D to 2, E to 4, F to 6, and G to 7. (You should check that the lines also correspond.)