Nearly neighbourly families of standard boxes

Abstract

It is demonstrated that each nearly neighbourly family of standard boxes in ${\mathbb{R}}^3$ has at most 12 elements. A combinatorial classification of all such families that have exactly 12 elements is given. All families satisfying an extra property called incompressibility are described. Compressible families are discussed briefly.

arXiv comment37 pages, 10 figures, 22 tables