The translative kissing number of tetrahedra is 18 (Q1302039)

The author shows that the maximum number of mutually nonoverlapping translates of any tetrahedron \(T\) which touch \(T\) is 18, and moreover this optimal touching arrangement is unique. This proves a conjecture of Ch. Zong from 1996. The analogous problem for the 3-ball is the famous Newton-Gregory problem from 1694, which gives a flavor of the difficulty of the problem.