Problem dossier · Geometry & Packing
Kissing numbers in higher dimensions
How many unit spheres can simultaneously touch a central unit sphere in dimension d without overlapping?
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Status
Known exactly only for d = 1–4 (2, 6, 12, 24), d = 8 (240) and d = 24 (196560). Wide gaps between constructions and SDP bounds for d = 5–7.
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§2
The Angle of Attack
Search lattice and code-based configurations in d = 5–7 to raise lower bounds; replicate and probe semidefinite-programming upper bounds for slack.
Tags: sphere packing · lattices · sdp · codes
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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Related Problems
More open problems in Geometry & Packing and adjacent territory.
- Borsuk's problem in low dimensions — Geometry & Packing
- Hadamard's maximal determinant problem — Geometry & Packing
- Square packing in a square — Geometry & Packing
- Tammes problem — Geometry & Packing
- Finite lattice representation problem — Algebra