Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs
Two d-polyhedra in \(E^ d\) are nearly-neighborly if they are separated by a hyperplane which contains a facet of each. The main result is: there can be at most 15 mutually nearly-neighborly tetrahedra in \(E^ 3\). There is a glossary of results on nearly-neighborly (and neighborly) sets of polyhedra, several conjectures, relevant results on decomposition of certain graphs. The paper ends with the following ``Note added in proof. Using a similar yet more detailed approach, S. Furino, B. Gamble and J. Zako (sic) proved that there can be at most 14 nearly-neighborly tetrahedra in \(E^ 3\).''
scientific article; zbMATH DE number 4062044
scientific article