title: Symmetry, topology and the maximum number of mutually pairwise-touching infinite cylinders: configuration classification.
abstract: 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 dimensions independently of 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.
authors.affiliation: Seoul National University , Seoul 151-742 , Korea.
authors.forename: Peter V
authors.identifier: 0000-0002-9837-5788
authors.initials: PV
authors.lastname: Pikhitsa
authors.affiliation: Seoul National University , Seoul 151-742 , Korea.
authors.forename: Stanislaw
authors.initials: S
authors.lastname: Pikhitsa
keywords: chirality matrix; mutually touching cylinders; topological invariant