Describe a finite model such that no two lines have the same set of incident points, axioms I2 and I3 are true, but I1 is false.

Describe a finite model such that no two lines have the same set of incident points, axioms I2 and I3 are true, but I1 is false.

Can you give a model as above with the additional constraint that for any two points, there are at least two lines incident to both?

I1: For any two points, there is a unique line incident to both.

I2: For every line, there are at least two points incident to it.

I3: There exist three non-collinear points