Reversible Pairs of Figures

  • Jin Akiyama
  • Kiyoko Matsunaga


I have here two figures: one is a shrimp and the other is a bream (Fig. 4.1.1). In Japan, there is a well-known saying, “throw a shrimp to catch a bream” which has same meaning as “throw a sprat to catch a mackerel” in English.


Equilateral Triangle Convex Polygon Reversible Transformation Checkerboard Pattern Reversible Figure 
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  1. [1]
    T. Abbott, Z. Abel, D. Charlton, E. Demaine, M. Demaine, S. Kominers, Hinged dissections exist, Discrete & Computational Geometry 47 (1) (2012), 150-186.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    J. Akiyama, Catalog of the Exhibition Held at Yoshii Gallery in Paris (2012)Google Scholar
  3. [3]
    J. Akiyama, F. Hurtado, C. Merino and J. Urrutia, A Problem on Hinged Dissections with Colours, Graphs and Combinatorics 20 (2), (2004), 145-159MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    J. Akiyama and S. Langerman, Parcel Magic, to be publishedGoogle Scholar
  5. [5]
    J. Akiyama and G. Nakamura, Dudeney Dissections of Polygons. Discrete and Computational Geometry, Lecture Notes in Computer Science, 1763, (2000), 14-29, SpringerMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    J. Akiyama and G. Nakamura, Congruent Dudeney Dissections of Triangles and Convex Quadrangles—All Hinge Points Interior to the Sides of the Polygons, Discrete and Computational Geometry, The Goodman-Pollack Festschrift. (B. Aronov, S. Basu, J. Pach and M. Sharir, eds.), Algorithms and Combinatorics, 25 (2003), 43-63, SpringerGoogle Scholar
  7. [7]
    J. Akiyama and G. Nakamura, Congruent Dudeney Dissections of Polygons – All the Hinge Points on Vertices of the Polygon, Discrete and Computationa1 Geometry, Lecture Notes in Computer Science, 2866 14-21 (2003), SpringerMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    J. Akiyama, D. Rappaport and H. Seong, A decision algorithm for reversible pairs of polygons, Disc. Appl. Math. 178, (2014), 19-26MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    J. Akiyama and H. Seong, A criterion for a pair of convex polygons to be reversible, Graphs and Combinatorics 31(2) (2015), 347-360.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    J. Akiyama and T. Tsukamoto, Envelope Magic, to appearGoogle Scholar
  11. [11]
    E. D. Demaine, M. L. Demaine, D. Eppstein, G. N. Frederickson, E. Friedman, Hinged dissection of polynominoes and polyforms, Comput. Geom. Theory Appl., 31 (3) (2005), 237-262CrossRefMATHGoogle Scholar
  12. [12]
    H. E. Dudeney, The Canterbury Puzzles and Other Curious Problems, W. Heinemann (1907)Google Scholar
  13. [13]
    G. N. Frederickson, Hinged Dissections: Swinging and Twisting, Cambridge University Press, 2002.MATHGoogle Scholar
  14. [14]
    R. Sarhangi, Making patterns on the surfaces of swing-hinged dissections, in Proceedings of Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, Leeuwarden, the Netherlands, July 2008.Google Scholar
  15. [15]
    D. Schattschneider, Will It Tile? Try the Conway Criterion, Mathematics Magazine Vol. 53 (Sept. 1980), No. 4, 224-233MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Wikipedia, Conway Criterion,

Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Kiyoko Matsunaga
    • 2
  1. 1.Tokyo University of ScienceTokyoJapan
  2. 2.YokohamaJapan

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