  Motivated by frequency assignment in office blocks, we study the chromatic
number of the adjacency graph of $3$-dimensional parallelepiped arrangements.
In the case each parallelepiped is within one floor, a direct application of
the Four-Colour Theorem yields that the adjacency graph has chromatic number at
most $8$. We provide an example of such an arrangement needing exactly $8$
colours. We also discuss bounds on the chromatic number of the adjacency graph
of general arrangements of $3$-dimensional parallelepipeds according to
geometrical measures of the parallelepipeds (side length, total surface or
volume).

Combinatorics