Skip to main content
SpringerLink
Log in

Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid

  • Conference paper
WALCOM: Algorithms and Computation (WALCOM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8973))

Included in the following conference series:

Abstract

Common unfolding of a regular tetrahedron and a Johnson-Zalgaller solid is investigated. More precisely, we investigate the sets of all edge unfoldings of Johnson-Zalgaller solids. Among 92 Johnson-Zalgaller solids, some of edge unfolding of J17 and J84 admit to fold into a regular tetrahedron. On the other hand, there are no edge unfolding of the other Johnson-Zalgaller solids that admit to fold into a regular tetrahedron.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akiyama, J.: Tile-Makers and Semi-Tile-Makers. The Mathematical Association of Amerika, Monthly 114, 602–609 (2007)

    MATH  MathSciNet  Google Scholar 

  2. Akiyama, J., Kuwata, T., Langerman, S., Okawa, K., Sato, I., Shephard, G.C.: Determination of All Tessellation Polyhedra with Regular Polygonal Faces. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds.) CGGA 2010. LNCS, vol. 7033, pp. 1–11. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Akiyama, J., Nara, C.: Developments of Polyhedra Using Oblique Coordinates. J. Indonesia. Math. Soc. 13(1), 99–114 (2007)

    MATH  MathSciNet  Google Scholar 

  4. Bobenko, A.I., Izmestiev, I.: Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes. arXiv:math.DG/0609447 (February 2008)

    Google Scholar 

  5. Demaine, E.D., O’Rourke, J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press (2007)

    Google Scholar 

  6. Horiyama, T., Shoji, W.: Edge unfoldings of Platonic solids never overlap. In: Proc. CCCG 2011, pp. 65–70 (2011)

    Google Scholar 

  7. Horiyama, T., Shoji, W.: The Number of Different Unfoldings of Polyhedra. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) ISAAC 2013. LNCS, vol. 8283, pp. 623–633. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Horiyama, T., Uehara, R.: Nonexistence of Common Edge Developments of Regular Tetrahedron and Other Platonic Solids. In: Proc. China-Japan Joint Conference on Computational Geometry, Graphs and Applications (CGGA 2010), pp. 56–57 (2010)

    Google Scholar 

  9. Kane, D., Price, G.N., Demaine, E.D.: A pseudopolynomial algorithm for Alexandrov’s Theorem. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 435–446. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. O’Rourke, J.: How to Fold It: The Mathematics of Linkage, Origami and Polyhedra. Cambridge University Press (2011)

    Google Scholar 

  11. Schattschneider, D.: The plane symmetry groups: their recognition and notation. American Mathematical Monthly 85, 439–450 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  12. Shirakawa, T., Horiyama, T., Uehara, R.: Construct of Common Development of Regular Tetrahedron and Cube. In: Proc. EuroCG 2011, pp. 47–50 (2011)

    Google Scholar 

  13. Strauss, W.S., Dürer, A.: The Painter’s Manual. Abaris Books (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Japan Tessellation Design Association, Japan

    Yoshiaki Araki

  2. Information Technology Center, Saitama University, Japan

    Takashi Horiyama

  3. School of Information Science, Japan Advanced Institute of Science and Technology, Japan

    Ryuhei Uehara

Authors
  1. Yoshiaki Araki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takashi Horiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ryuhei Uehara
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of CSE, BUET, ECE Building, West Palasi, 1205, Dhaka, Bangladesh

    M. Sohel Rahman

  2. The Advanced Algorithms Research Laboratory, The University of Electro-Communications, Chofugaoka 1-5-1, 182-8585, Chofu, Tokyo, Japan

    Etsuji Tomita

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Araki, Y., Horiyama, T., Uehara, R. (2015). Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15612-5_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15611-8

  • Online ISBN: 978-3-319-15612-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation