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Geometry and Crystallography of Self-Supporting Rod Structures

  • Conference paper
Katachi ∪ Symmetry

Abstract

Cylindrical rods with long enough are arranged in some order. The motivation is to construct a generalized crystallography, which unifies periodic and nonperiodic arrangements. It serves as compilation of basic knowledge of arranging and packing, which are fundamental phenomena in physical world. A systematic investigation is done focusing on the possible periodic arrangements of rods taking only six directions. The possible structures are exhaustively studied within a certain condition. It is described in Part I.

In Part II, some description of the related miscellaneous things are given from interdisciplinary viewpoint or for the purpose to see science among culture.

The mathematical part will be published elsewhere.

The article is based on two presentations at the symposium 1: Y. Teshima, Y. Watanabe, and T. Ogawa; The Periodic Six-Axes-Structures in Rod System. 2: T. Ogawa; Puzzle, Science, Culture: Taking Rod Constructions as an Example.

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References

  1. L. Fejes Tóth; Lagerungen in der Ebene, auf der Kugel und im Raum, Springer-Verlag, 1972. (Japanese translation): Haichi no MondaiHeimen, kyūmen, kūkan ni okern translated by I. Higuchi and M. Tanemura, Misuzu Shobō, 1983. (This contains lots of notes and an attractive postscript by tranlatorp’.)

    Google Scholar 

  2. Masaharu Tanemura, “On Random Complete Packing by Discs”, Ann. Inst. Stat. Math., 31B, 1979, pp. 351–365. M. Hasegawa and M. Tanemura, Nawabari no Scitaigaku: Scitai no Model to Kuukan Pattern no Toukei (in Japanese, The Ecology of Territory: Statistics of Biological Model and Spatial Pattern), Tokai University Press, 1986.

    Google Scholar 

  3. M. O’Keeffe and Anderson, “Rod Packings and Crystal Chemistry”, Acta Cryst. A33, 1977, pp. 914–923. M. O’Keeffe: “Cubic Cylinder Packing”, Acta Cryst. A48, 1972, pp. 879-884.

    Article  Google Scholar 

  4. A. Hijikata and K. Fukuta, Nihon Fukugō Zairyō Gakkai Shi (in Japanese, J. Jpn. Soc. for Composite Materials), 18, 1992, pp. 231–238. Kenji Fukuta, Nihon Fukugō Zairyō Gakkai Shi (in Japanese, J. Jpn. Soc. for Composite Materials), 21, 1995, pp. 51-60.

    Article  Google Scholar 

  5. T. Ogawa, Y. Teshima, and Y. Watanabe, Nihon Fukugō Zairyō Gakkai Shi (in Japanese, J. Jpn. Soc. for Composite Materials), 21, 1995, 165–173.

    Article  Google Scholar 

  6. S. T. Coffin: “The Puzzling World of Polyhedral Dissections”, Oxford University Press, 1990, pp. 132–142

    Google Scholar 

  7. Akio Hizume, “Hoshikago (Starcage)” (in Japanese) in Katachi no Bunka-shi 1: Asia no Katachi wo yomu, Kōsakusha, 1993, pp. 208–225. Akio Hizume, “Star Cage: New Dimension of the Penrose Lattice” Forma, 9, 259-272 (1994).

    Google Scholar 

  8. T. Ogawa, “Rittai Tajikuori (3-D Multi-Axes Weavings)” (in Japanese) in Katachi no Bunka-shi 1: Asia no Katachi wo yomu, Kōsakusha, 1993, pp. 226–235.

    Google Scholar 

  9. Roger Penrose: “The Role of Aesthetics in Pure and Applied Mathematical Research”, J. Institute of Mathematics and its Applications, 12, 1974, 266–271.

    Google Scholar 

  10. Polanyi, Michael; The Tacit Dimension, Routledge & Kegan Paul Ltd., London, 1966.

    Google Scholar 

  11. T. Ogawa and Y. Nakajima, “Flustration, Degeneracy, and Forms — A View of the Antiferromagnetic Ising Model on a Triangular Lattice”, Prog. Theor. Phys. Suppl. No. 87, 1986, pp. 90–101. T. Ogawa, M. Himeno, and T. Hirata, “Ideal Critical Patterns; An Attempt Concerning Lenz-Ising Model and Visual Images”, Forma, 6, 1991, 129-140.

    Article  Google Scholar 

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© 1996 Springer-Verlag Tokyo

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Ogawa, T., Teshima, Y., Watanabe, Y. (1996). Geometry and Crystallography of Self-Supporting Rod Structures. In: Ogawa, T., Miura, K., Masunari, T., Nagy, D. (eds) Katachi ∪ Symmetry. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68407-7_26

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  • DOI: https://doi.org/10.1007/978-4-431-68407-7_26

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68409-1

  • Online ISBN: 978-4-431-68407-7

  • eBook Packages: Springer Book Archive

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