• Ryuhei UeharaEmail author


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.


  1. [Gol96]
    S.W. Golomb, Polyominoes: Puzzles Problems, and Packings (Princeton University, Patterns, 1996)Google Scholar
  2. [Gar08]
    M. Gardner. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi (Cambridge, 2008)Google Scholar
  3. [Gar14]
    M. Gardner, Knots and Borromean Rings, Rep-Tiles, and Eight Queens (Cambridge, 2014)Google Scholar
  4. [ABD+17]
    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. [Tor92]
    P. Torbijn, Cubic hexomino cubes, in Cubism for Fun, vol. 30 (1992), pp. 18–20Google Scholar
  6. [Tor02]
    P. Torbijn, Covering a cube with congruent polyominoes, in Cubism for Fun, vol. 58 (2002), pp. 18–20Google Scholar
  7. [Tor02b]
    P. Torbijn, Covering a cube with congruent polyominoes (2), in Cubism for Fun, vol. 59 (2002), p. 14Google Scholar
  8. [Tor03]
    P. Torbijn, Covering a cube with congruent polyominoes (3), in Cubism for Fun, vol. 61 (2003), pp. 12–16Google Scholar
  9. [XHU17]
    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. 62–67Google Scholar
  10. [Xu17]
    D. Xu, Research on Developments of Polycubes. Ph.D. thesis, School of Information Science, JAIST (2017)Google Scholar
  11. [DO07]
    E.D. Demaine, J. O’Rourke, Geometric Folding Algorithms: Linkages, Origami Polyhedra (Cambridge, 2007)Google Scholar
  12. [AHU16]
    Y. Araki, T. Horiyama, R. Uehara, Common unfolding of regular tetrahedron and johnson-zalgaller solid. J. Graph Algor. Appl. 20(1), 101–114 (2016)MathSciNetCrossRefGoogle Scholar
  13. [Ser00]
    R. Séroul, 2.2. prime number and sum of two squares, in Programming for Mathematicians (Springer, Berlin, 2000), pp. 18–19Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.JAISTIshikawaJapan

Personalised recommendations