Abstract
We report a new periodic structure of the cylinder packing. All the cylinders are congruent and the length of the cylinders are infinite and their directions are restricted to only six directions opf (110). Each cylinder is fixed by cylinders of other directions, so that the whole structure sustains mechanical stability. The packing density equals to \( \frac{{(351\sqrt 2 - 108\sqrt 6 )\pi }} {{1936}}( \simeq 0.376219)\), which lies between two values ever known: 0.494 or 0.247. The arrangement of parallel cylinders forms a certain 2D rhombic lattice common to all of six (110) directions. Nevertheless the way of fixing cylinders is different in all of six directions: the cylinders of two directions are supported with the rhombus-type, and the cylinders of other four directions are supported with the equilateral-triangle-type. The structure containing the equilateral-triangle-type has never been known.
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Teshima, Y., Watanabe, Y., Ogawa, T. (2001). A New Structure of Cylinder Packing. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_33
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DOI: https://doi.org/10.1007/3-540-47738-1_33
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