Axioms for the Three Point Geometry:

1. There exist exactly 3 points in this geometry.

2. Two distinct points are on exactly one line.

3. Not all the points of the geometry are on the same line.

4. Two distinct lines are on at least one point.

Can someone come up with a shape that satisfies axioms 1-3 but not 4? Trying to show that the axioms are independent and I've gotten every one except axiom 4.

Thx!