For each n from 8 through 2700 there is a locally area-minimizing three-chamber partition whose interface blows down to a singular cone, so the lens is not unique.
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On the non-uniqueness of locally minimizing clusters via singular cones
For each n from 8 through 2700 there is a locally area-minimizing three-chamber partition whose interface blows down to a singular cone, so the lens is not unique.