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 dimensions independently of the shape of the cylinder cross-sections....

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Bibliographic Details
Published in:Royal Society open science 2017-01, Vol.4 (1), p.160729-160729
Main Authors: Pikhitsa, Peter V., Pikhitsa, Stanislaw
Format: Article
Language:English
Subjects:
Chirality Matrix
Mathematics
Mutually Touching Cylinders
Topological Invariant
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Summary: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.
ISSN:2054-5703
2054-5703
DOI:10.1098/rsos.160729