The kissing numbers of tetrahedra (Q1913596)

The author shows that there is a lattice packing of tetrahedra such that each tetrahedron contacts 18 others, and that any other packing lattice permits a smaller contact- or kissing-number. So he solves the lattice kissing number problem for the tetrahedron completely. The kissing number for the tetrahedron is remarkably larger than that of the 3-ball, which is 12 according to the famous Newton-Gregory problem. Another surprising phenomenon: The kissing number in the densest lattice packing of tetrahedron is 14, i.e. considerably smaller than the optimum; in contrast to the sphere-case.