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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.

SUBMITTER: Pikhitsa PV

PROVIDER: S-EPMC5319341 | biostudies-literature | 2017 Jan

REPOSITORIES: biostudies-literature

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Symmetry, topology and the maximum number of mutually pairwise-touching infinite cylinders: configuration classification.

Pikhitsa Peter V PV Pikhitsa Stanislaw S

Royal Society open science 20170118 1

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, whi ...[more]

PMID: 28280575

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