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Affine Equivalent Classes of Parallelohedra

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Computational Geometry, Graphs and Applications (CGGA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7033))

Abstract

In the paper the affine equivalence relation in the set of parallelohedra is studied. One proves the uniqueness theorem for a wide class of d-dimensional parallelohedra. From here it follows that for every d ( ≥ 2) the space of affine equivalent classes of d-dimensional primitive parallelohedra has dimension d(d + 1)/2 − 1.

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Russian Academy of Science, ul. Gubkina 8, Moscow, 119991, Russia

    Nikolai Dolbilin

  2. Faculty of Education, Kumamoto University, Kumamoto, 860-8555, Japan

    Jin-ichi Itoh

  3. Liberal Arts Education Center, Aso Campus, Tokai University, Aso, Kumamoto, 869-1404, Japan

    Chie Nara

Authors
  1. Nikolai Dolbilin
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  2. Jin-ichi Itoh
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  3. Chie Nara
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Tokio, Shibuya-ku, Japan

    Jin Akiyama

  2. School of Computer Science and Technology, Dalian Maritime University, 116026, Dalian, China

    Jiang Bo

  3. Ibaraki University, Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Mikio Kano

  4. Tokai University, 4-1-1 Kitakaname, 259-1292, Hiratsuka, Japan

    Xuehou Tan

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© 2011 Springer-Verlag Berlin Heidelberg

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Dolbilin, N., Itoh, Ji., Nara, C. (2011). Affine Equivalent Classes of Parallelohedra. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-24983-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24982-2

  • Online ISBN: 978-3-642-24983-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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