Fishburn and Reeds [FiRe92] also proved that the smallest $n$ for which there exists
a convex $n$-gon and a cut $\{A, B\}$ of its vertices such that $|\{b \in B : d(a, b) = 1\}| ≥ 3$
for all $a \in A$, and $|\{a \in A : d(a, b) = 1\}| ≥ 3$ for all $b \in B$, is $n = 20$.
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theorem erdos_97.variants.three_unit_distance_cut_min :
sInf {n : ℕ | ∃ (V : Finset ℝ²) (A B : Finset ℝ²),
n = V.card ∧ ConvexIndep V ∧ A.Nonempty ∧ B.Nonempty ∧ IsCut V A B ∧
HasNUnitDistancePointsOn 3 B A ∧ HasNUnitDistancePointsOn 3 A B} = 20
