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Non-convex unit-edge polytopes on kissing configurations in dimensions 5-7
All nine known conjecturally optimal non-lattice kissing configurations in dimensions 5, 6, and 7 are the vertex sets of polytopes with only unit edges. Eight of the nine are non-convex, and the contact polytopes, the convex hulls of the same points, have longer edges. The edges of the unit-edge pol
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