Tessellation Polyhedra

  • Jin Akiyama
  • Kiyoko Matsunaga


Among the infinitely many convex polyhedra that exist, there are some whose faces are all regular polygons. They are called “regular faced polyhedra” (RFP for short). Can you guess how many such polyhedra there are?


Equilateral Triangle Convex Polyhedron Regular Polygon Interior Angle Regular Hexagon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    J. Akiyama, T. Kuwata, S. Langerman, K. Okawa, I. Sato and G. C. Shephard, Determination of All Tessellation Polyhedra with Regular Polygonal Faces, LNCS 7033 (2011), 1-11, SpringerMathSciNetMATHGoogle Scholar
  2. [2]
    P. Brass, W. O. J. Moser and J. Pach, Research Problems in Discrete Geometry, Springer-Verlag (2005)MATHGoogle Scholar
  3. [3]
    S. Hitotumatu, Investigate What Platonic Solids Are (Seitamentai wo Toku)(in Japanese), Tokai Univ. Press (1983)Google Scholar
  4. [4]
    N. W. Johnson, Convex polyhedra with regular faces, Canad. J. Math. 18 (1966), 169-200MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    C. A. Pickover, The Mαth βook, Sterling (2009)Google Scholar
  6. [6]
    G. C. Shephard, Tessellation polyhedra, Symmetry, Culture and Science 22 (1-2), (2011), 65-82, Special issue, Tessellations, Part 1Google Scholar
  7. [7]
    E. W. Weisstein, Johnson solid, Math World — A Wolfram Web Resource,
  8. [8]
    D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, Penguin Books, London (1991)MATHGoogle Scholar
  9. [9]
    V. A. Zalgaller, Convex polyhedra with regular faces, Translated from Russian. Seminars in Mathematics, VA. Steklov Mathematical Institute, Leningrad, vol. 2 (1969), Consultants Bureau, New YorkGoogle Scholar
  10. [10]
    E.W. Weisstein, CRC Concise Encyclopedia of MATHEMATICS, CRC Press (1999)MATHGoogle Scholar

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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