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Matthew Self

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Preprint Sep 2026

Non-convex polytopes realizing kissing contact graphs in dimensions 5-7

Each of the 12 known conjecturally optimal kissing configurations in dimensions 5, 6, and 7 carries a contact-graph polytope: a polytope whose vertices are the configuration points and whose edges are exactly its contacts. Eight of these polytopes are non-convex and distinct from their convex hulls, which include longe...

Matthew Self · 0 citations