  We provide a complete classification of possible configurations of mutually
pairwise touching infinite cylinders in Euclidian 3D space. It turns out that
there is a maximum number of such cylinders possible in 3D independently on the
shape of the cylinder cross-sections. We give the explanation of the uniqueness
of the non-trivial configuration of seven equal mutually touching round
infinite cylinders found earlier. Some results obtained for the chirality
matrix which is equivalent to the Seidel adjacency matrix may be found useful
for the theory of graphs.
