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Symmetry of Platonic Solids

  • Jin Akiyama
  • Kiyoko Matsunaga
Chapter

Abstract

Platonic solids have many beautiful properties, because they are highly symmetric.

Remember the ones we discussed in the previous chapter? Now, I will show you a few more results which relate to the symmetry of Platonic solids.

Let's start with the lengths of diagonals.

Keywords

Regular Tetrahedron Soccer Ball Platonic Solid Regular Pentagon Regular Octahedron 
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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References

  1. [1]
    J. Akiyama, Let's go, Math. (Soreike Sansu) (in Japanese), NHK Publishing (1999)Google Scholar
  2. [2]
    J. Akiyama and G. Nakamura, Solids Through Reflecting Mirrors, Teaching Mathematics and Its Applications 19 (2), Oxford University Press (2000), 62-68CrossRefGoogle Scholar
  3. [3]
    J. Akiyama and I. Sato, On the diagonal weights of inscribed polytopes, Elemente der Mathematik, 68 (3), (2013), 89-92, European Math Soc.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    T. Betsumiya and G. Nakamura, A Solid Model for Penrose Tiling, The Int'l Katachi and Symmetry Symposium, Tsukuba University (1993)Google Scholar
  5. [5]
    M. Deza, H. Maehara, A few applications of negative type inequalities, Graphs and Combinatorics 10 (1994), 255-262MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    R. Honsberger, Mathematical Diamonds, The Mathematical Association of America (2003)MATHGoogle Scholar
  7. [7]
    H. Murayama and M. Takahashi, How far has the truth about the Universe been investigated, Dr. Murayama? (Murayama-san, Uchū wa dokomade Wakattandesuka?)(in Japanese), Asahishimbun, (2013)Google Scholar
  8. [8]
    I. Stewart, What Shape is a Snowflake?, Ivy Press Ltd. (2001)Google Scholar
  9. [9]
    K. Tsubota et al., 50 Curious topics and models to intrigue students (Manabu Iyokuwo Takameru Sansu Omoshiro Kyouzai Kyougu 50 Sen) (in Japanese), Meiji Tosho (1996)Google 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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