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Section 1.5 Fano Geometry

Figure 1.5.1. A model for the Fano geometry.

A well-known geometric model for incidence geometry is shown in Figure 1.5.1. This model is known both as the Fano geometry and as the seven-point projective plane.

How many lines are there in this geometry? Is the circle a line?

How many lines are there in the Fano geometry that contain the point \(D\) and are parallel to the line through the points \(A\text{,}\) \(B\text{,}\) and \(C\text{?}\)