Skip to main content

Rep-Cube

  • Chapter
  • First Online:
Introduction to Computational Origami

Abstract

In this chapter, we introduce a new concept of rep-cube and its known results. It is a fledgling concept born in 2016, so there are many topics to be studied.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    Note that “rep-tile” is the word play of “reptile”.

  2. 2.

    In fact, Solomon W. Golomn was born in 1932 and passed away in 2016. We gave the name to mourn it. Later, earlier research in the puzzle society was found the same concept as rep-cube. See [Tor92, Tor02, Tor02b, Tor03] for further details.

References

  1. S.W. Golomb, Polyominoes: Puzzles Problems, and Packings (Princeton University, Patterns, 1996)

    Google Scholar 

  2. M. Gardner. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi (Cambridge, 2008)

    Google Scholar 

  3. M. Gardner, Knots and Borromean Rings, Rep-Tiles, and Eight Queens (Cambridge, 2014)

    Google Scholar 

  4. Z. Abel, B. Ballinger, E.D. Demaine, M.L. Demaine, J. Erickson, A. Hesterberg, H. Ito, I. Kostitsyna, J. Lynch, R. Uehara, Unfolding and dissection of multiple cubes, tetrahedra, and doubly covered squares. J. Inf. Process. 25, 610–615 (2017)

    Google Scholar 

  5. P. Torbijn, Cubic hexomino cubes, in Cubism for Fun, vol. 30 (1992), pp. 18–20

    Google Scholar 

  6. P. Torbijn, Covering a cube with congruent polyominoes, in Cubism for Fun, vol. 58 (2002), pp. 18–20

    Google Scholar 

  7. P. Torbijn, Covering a cube with congruent polyominoes (2), in Cubism for Fun, vol. 59 (2002), p. 14

    Google Scholar 

  8. P. Torbijn, Covering a cube with congruent polyominoes (3), in Cubism for Fun, vol. 61 (2003), pp. 12–16

    Google Scholar 

  9. D. Xu, T. Horiyama, R. Uehara, Rep-cubes: unfolding and dissection of cubes, in The 29th Canadian Conference on Computational Geometry (CCCG 2017) (Ottawa, Canada, 2017), pp. 62–67

    Google Scholar 

  10. D. Xu, Research on Developments of Polycubes. Ph.D. thesis, School of Information Science, JAIST (2017)

    Google Scholar 

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

    Google Scholar 

  12. Y. Araki, T. Horiyama, R. Uehara, Common unfolding of regular tetrahedron and johnson-zalgaller solid. J. Graph Algor. Appl. 20(1), 101–114 (2016)

    Article  MathSciNet  Google Scholar 

  13. R. Séroul, 2.2. prime number and sum of two squares, in Programming for Mathematicians (Springer, Berlin, 2000), pp. 18–19

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ryuhei Uehara .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Uehara, R. (2020). Rep-Cube. In: Introduction to Computational Origami. Springer, Singapore. https://doi.org/10.1007/978-981-15-4470-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-4470-5_9

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-4469-9

  • Online ISBN: 978-981-15-4470-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics