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Volume 35, Number 3, pages 373-376 (2024)
https://doi.org/10.26830/symmetry_2024_3_373
IKEGAMI’S 3D JIGSAW PUZZLES AND SYMMETRY OF THEIR PUZZLE PIECES
Yoshinori Teshima1, Yuki Machiya2, Kenji Yamazawa3, Yuji Ikegami4
1 Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016, Japan.
Email: yoshinori.teshima@it-chiba.ac.jp
2 Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016, Japan.
Email: s1421295MH@s.chibakoudai.jp
3 RIKEN, 2-1 Hirosawa Wakou, Saitama 351-0198, Japan.
Email: kyama@riken.jp
4 RIKEN, 2-1 Hirosawa Wakou, Saitama 351-0198, Japan.
Email: yikegami@riken.jp
Abstract: A 3D jigsaw puzzle is a three-dimensional version of an ordinary 2D jigsaw puzzle, and the similar concavo-convex curved lines on its surface with ordinarily 2D jigsaw puzzle. Ikegami’s 3D jigsaw puzzle was developed by Yuji Ikegami in 2000. He succeeded in developing an epoch-making 3D jigsaw puzzle by applying a traditional wooden joint (Watanabe, Ikegami et al., 2006). The name of the joint he applied is Shihou-tsugi, whic is a kind of traditional wooden joint. The cross section of the tenons appears on four faces of the square column, and they seem to intersect each other. But inside, two tenons are arranged at an angle of 45 degrees to the surface of the square column and can slide along that direction. If the shape of a tenon inside the Ikegami's 3D jigsaw puzzle is approximated by a cylinder, it can be seen that the cylinder arrangement is hidden inside the puzzle. Cylinders in three different directions are arranged without intersecting. A 3D jigsaw puzzle with such a structure is called an Ikegami's 3D jigsaw puzzle. The design of the Ikegami's 3D jigsaw puzzle is essentially related to the periodic configuration of cylinders in 3D space (Teshima et al., 2001; O’Keefe et al., 2001; Teshima & Matsumoto, 2012).
References:
O'Keeffe, M., Plevert, J., Teshima, Y., Watanabe, Y. & Ogawa, T., (2001) The invariant cubic rod packings: symmetries and coordinates, Acta Crystallographica, A57, pp. 110-111. https://doi.org/10.1107/S010876730001151X
Teshima, Y., Watanabe, Y. & Ogawa, T., (2001) A new structure of cylinder packing, Lecture Notes in Computer Science, 2098, pp.351-361. https://doi.org/10.1007/3-540-47738-1_33
Teshima, Y. & Matsumoto, T., (2012) Space Group of Heterogeneous Cylinder Packing with Six <110> Directions, Glass Physics and Chemistry, 38-1, pp.41-48. https://doi.org/10.1134/S1087659612010142
Watanabe, Y., Ikegami, Y., Yamazawa, K., Murakami, Y., (2006) World of Scientific Puzzle Art Using Layer Manufacturing, Forma, 21-1, p.37-48.
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