Four line geometry is a finite geometry subject to the following three axioms:
1. there exist exactly four lines,
2. any two distinct lines have exactly one point of on both of them, and
3. each point is on exactly two lines.
Four line geometry is categorical.
Like many finite geometries, the number of provable theorems in three point geometry is small. Of those, one can prove that there exist exactly six points and that each line has exactly three points on it. In that regard, four line geometry is among the simplest finite geometries.
Note that by forming the plane dual of the four line geometry axioms (that is, by interchanging the terms "point" and "line" throughout the above discussion), one obtains axioms for a four point geometry. In this new (but equivalent) geometry, the plane duals of the above results still hold.
