Supplementary docx file contains a collection of possible configurations of mutually touching 7 and 9 cylinders together with their topological characteristics in Appendices 1-4. Appendix 5 gives the text of a Mathcad program that calculates the chirality matrices of different dimensions that do not contain K5. from Symmetry, topology and the maximum number of mutually pairwise-touching infinite cylinders: configuration classification

We provide a complete classification of possible configurations of mutually pairwise touching infinite cylinders in Euclidian three-dimensional space. It turns out that there is a maximum number of such cylinders possible in three-dimensional 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.