__Fe-Fo Geometry__

**Undefined terms:** Fe's, Fo's, and the relation "belongs to."

**Axiom 1.** There exist exactly three distinct Fe's in this system.

**Axiom 2.** Any two distinct Fe's belong to exactly one Fo.

**Axiom 3.** Not all Fe's belong to the same Fo.

**Axiom 4.** Any two distinct Fo's contain at least one Fe that belongs to both.

I was able to create a model for this Fe-Fo Geometry:

**Axiom 1.** There are exactly three people.

**Axiom 2.** Two distinct people belong to exactly one committee.

**Axiom 3.** Not all people belong to the same committee.

**Axiom 4.** Any two distinct committees contain one person who belongs to both.

An example of a "non-model" would be as follows...

**Axiom 1.** There are exactly three books.

**Axiom 2.** Any two books are on exactly one shelf.

**Axiom 3.** Not all books are on the same shelf.

**Axiom 4.** Any two distinct shelves contain one book that is on both.

This is a "non-model" because it is not possible for a book to be on two shelves at the same time. Axioms 2 and 4 are not "correct" statements.

*We are almost to my question...*

__Four-Point Geometry__

**Axiom 1.** There exist exactly four points

**Axiom 2.** Any two distinct points have exactly one line on both of them.

**Axiom 3.** Each line is on exactly two points.

*My question is... What would be an example of a model and a "non-model" for Four-Point Geometry? I have attached a drawing that represents Four-Point Geometry. I am sorry for the long read.*