The three point geometry
There are exactly three points.
Any two distinct points are both on exactly one line.
All three points are not on the same line.
Every line has at least two points on it.
A model
A model: the three point pizza shop
There are exactly three toppings.
Any two distinct toppings are both on exactly one pizza.
All three toppings are not on the same pizza.
Every pizza has at least two toppings on it.