No Nine Neighborly Tetrahedra Exist
Joseph Zaks
Jan 1991 · American Mathematical Society: Memoirs of the American Mathematical Society Ibhuku elingu-447 · American Mathematical Soc.
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A long standing conjecture of Bagemihl (1956) states that there can be at most eight tetrahedra in 3-space, such that every two of them meet in a two-dimensional set. We settle this conjecture affirmatively. We get some information on families of similar nature, consisting of eight tetrahedra. We present a joint result, showing that there can be at most fourteen tetrahedra in 3-space, such that for every two of them there is a plane which separates them and contains a facet of each one of them.
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