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Continuous Folding of Regular Dodecahedra

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Book cover Discrete and Computational Geometry and Graphs (JCDCGG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9943))

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Abstract

Itoh and Nara [3] discussed with Kobayashi the continuous flattening of all Platonic polyhedra; however, a problem was encountered in the case of the dodecahedron. To complete the study, we explicitly show, in this paper, a continuous folding of a regular dodecahedron following the ideas in [3].

J.-i. Itoh—Supported by Grant-in-Aid for Scientific Research(B) (15KT0020) and Scientific Research(C)(26400072).

N. Katoh—Supported by JSPS Grant-in-Aid for Scientific Research(A) (25240004).

Y. Kobayashi—Supported by JSPS Grant-in-Aid for Scientific Research(A) (25240004).

C. Nara—Supported by Grant-in-Aid for Scientific Research(C) (16K05258).

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References

  1. Abel, Z., Demaine, E., Demaine, M., Itoh, J., Lebiw, A., Nara, C., O’Rourke, J.: Continuously flattening polyhedra using straight skeletons. In: Proceedings of 30th Annual Symposium on Computational Geometry (SoCG), pp. 396–405 (2014)

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Author information

Authors and Affiliations

  1. Graduate School of Science and Engineering, Saitama University, Saitama, Japan

    Takashi Horiyama

  2. Faculty of Education, Kumamoto University, Kumamoto, 860-8555, Japan

    Jin-ichi Itoh

  3. Department of Inforatics, Faculty of Science and Technology, Kwansei Gakuin University, Nishinomiya, Japan

    Naoki Katoh

  4. JST, CREST, Tokyo, Japan

    Naoki Katoh & Yuki Kobayashi

  5. Graduate School of Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8550, Japan

    Yuki Kobayashi

  6. Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Tokyo, 164-8525, Japan

    Chie Nara

Authors
  1. Takashi Horiyama
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  2. Jin-ichi Itoh
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  3. Naoki Katoh
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  4. Yuki Kobayashi
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  5. Chie Nara
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Corresponding author

Correspondence to Chie Nara .

Editor information

Editors and Affiliations

  1. Tokyo University of Science , Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications , Tokyo, Japan

    Hiro Ito

  3. Tokai University , Tokyo, Japan

    Toshinori Sakai

  4. Osaka Prefecture University , Sakai, Japan

    Yushi Uno

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Horiyama, T., Itoh, Ji., Katoh, N., Kobayashi, Y., Nara, C. (2016). Continuous Folding of Regular Dodecahedra. In: Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science(), vol 9943. Springer, Cham. https://doi.org/10.1007/978-3-319-48532-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-48532-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48531-7

  • Online ISBN: 978-3-319-48532-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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