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Construct a geometric model using axioms

Construct a model that satisfies the following axioms.
- 1. There exists at least 1 line.
- 2. Every line of the geometry has exactly 4 points on it.
- 3. Not all points of the geometry are on the same line.
- 4. Each point of the geometry is contained in exactly 3 lines.
- 5. Every pair of lines intersect and their intersection is exactly 1 point.

Solution Summary

Axoims are used to construct a geometric model. A diagram is included.