Incidence geometry - Wikipedia: "Every triple of distinct points is incident with precisely one cycle.
For any flag (P, z) and any point Q not incident with z there is a unique cycle z∗ with P I z∗, Q I z∗ and z ∩ z∗ = {P}. (The cycles are said to touch at P.)
Every cycle has at least three points and there exists at least one cycle."
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