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Imaginary Hypercubes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

Abstract

Imaginary cubes are three-dimensional objects that have square projections in three orthogonal ways, just like a cube has. In this paper, we introduce higher-dimensional extensions of imaginary cubes and study their properties.

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References

  1. Tsuiki, H.: Imaginary cubes and their puzzles. Algorithms 5, 273–288 (2012)

    Article  MathSciNet  Google Scholar 

  2. Tsuiki, H.: Does it look square – hexagonal bipyramids, triangular antiprismoids, and their fractals. In: Proceedings of Conference Bridges Donostia, pp. 277–286. Tarquin Publications (2007)

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  3. Tsuiki, H.: Imaginary cubes–objects with three square projection images. In: Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture, pp. 159–166. Tessellations Publishing, Phoenix (2010)

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  4. Tsuiki, H.: SUDOKU colorings of the hexagonal bipyramid fractal. In: Ito, H., Kano, M., Katoh, N., Uno, Y. (eds.) KyotoCGGT 2007. LNCS, vol. 4535, pp. 224–235. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Ziegler, G.M.: Lectures on Polytopes. Springer, New York (1995)

    Book  MATH  Google Scholar 

  6. Okabe, A., Boots, B., Sugihara, K.: Spatial Tessellations Concepts and Applications of Voronoi Diagrams. Wiley, New York (1992)

    MATH  Google Scholar 

  7. Hutchinson, J.: Fractals and self similarity. Indiana Univ. Math. J. 30, 713–747 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  8. Coxeter, H.S.M.: Regular Polytopes. Dover, New York (1973)

    Google Scholar 

  9. McKay, B.D., Wanless, I.M.: A census of small latin hypercubes. SIAM J. Discrete Math. 22, 719–736 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Hideki Tsuiki .

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© 2014 Springer International Publishing Switzerland

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Tsuiki, H., Tsukamoto, Y. (2014). Imaginary Hypercubes. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_15

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  • DOI: https://doi.org/10.1007/978-3-319-13287-7_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13286-0

  • Online ISBN: 978-3-319-13287-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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