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No nine neighborly tetrahedra exist

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Publication:3210466
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DOI10.1090/memo/0447zbMath0723.52004OpenAlexW2053560871MaRDI QIDQ3210466

Joseph Zaks

Publication date: 1991

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0447


zbMATH Keywords

tetrahedraneighborly family


Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Three-dimensional polytopes (52B10) Software, source code, etc. for problems pertaining to convex and discrete geometry (52-04) Polyhedra and polytopes; regular figures, division of spaces (51M20)


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Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs ⋮ Putting convex \(d\)-polytopes inside frames ⋮ Two neighborly families of 3-pyramids and of 3-boxes in \(E^{3}\) ⋮ Neighborly families in \(E^d\) consisting of either \(d\)-pyramids over \((d-1)\)-cubes, or else of \(d\)-cubes ⋮ Nearly neighbourly families of standard boxes ⋮ No more than \(2^{d+1}-2\) nearly neighbourly simplices in \({\mathbb{R}}^d\) ⋮ Matchings and covers in hypergraphs



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