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Symmetry, topology and the maximum number of mutually pairwise-touching infinite cylinders: configuration classification
- Source :
- Royal Society Open Science, Royal Society Open Science, Vol 4, Iss 1 (2017)
- Publication Year :
- 2016
-
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.
- Subjects :
- 02 engineering and technology
Space (mathematics)
01 natural sciences
Cylinder (engine)
law.invention
Matrix (mathematics)
law
Seidel adjacency matrix
0103 physical sciences
chirality matrix
Uniqueness
mutually touching cylinders
lcsh:Science
Topology (chemistry)
Mathematics
010302 applied physics
Multidisciplinary
Mathematical analysis
021001 nanoscience & nanotechnology
Symmetry (physics)
topological invariant
Chirality (mathematics)
lcsh:Q
0210 nano-technology
Research Article
Subjects
Details
- ISSN :
- 20545703
- Volume :
- 4
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Royal Society open science
- Accession number :
- edsair.doi.dedup.....5189c5880795d902c9764d93b6329207