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Platonic Solids

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Abstract

The ancient Greek philosopher Plato loved five special polyhedral (Fig.5.1.1). These were the solids with equivalent faces composed of congruent regular convex polygons. Today, we know them as Platonic solids; and there are exactly five of them (Fig. 5.1.2).

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References

  1. M. Aigner and G. M. Zieglar, Proofs from THE BOOK, 4th ed., Springer (2010)

    Book  Google Scholar 

  2. S. Hitotumatu, Investigate What Platonic Solids Are (Seitamentai wo Toku) (in Japanese), Tokai Univ. Press (1983)

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  3. R. Padoicić, G. Tóth, The discharging method in combinatorial geometry and the Pach-Sharir conjecture, Contemporary Mathematics 453, (2008), 319-342

    Article  MathSciNet  MATH  Google Scholar 

  4. C. A. Pickover, The Mαth βook, Sterling (2009)

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  5. S. Roberts, King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry, Walker Publishing Company (2006)

    MATH  Google Scholar 

  6. M. Watanabe, Kepler and the Harmony of the Universe (Kepura to Sekai no Chouwa) (in Japanese), Kyoritsu Publishing (1991)

    Google Scholar 

  7. D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, Penguin, London (1991)

    MATH  Google Scholar 

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Akiyama, J., Matsunaga, K. (2015). Platonic Solids. In: Treks into Intuitive Geometry. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55843-9_5

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