Advertisement

Affine Classes of 3-Dimensional Parallelohedra - Their Parametrization -

  • Nikolai Dolbilin
  • Jin-ichi Itoh
  • Chie Nara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8296)

Abstract

In addition to the well-known classification of 3-dimensional parallelohedra we describe this important class of polytopes classified by the affine equivalence relation and parametrize representatives of their equivalent classes.

Keywords

Steklov Institute Uniqueness Theorem Combinatorial Type Equivalent Classis Rhombic Dodecahedron 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fedorov, E.S.: An introduction to the Theory of Figures, St. Petersburg (1885) (in Russian)Google Scholar
  2. 2.
    Minkowski, H.: Allgemeine Lerätze über die convexen Polyeder. Gött. Nachr., 198–219 (1897)Google Scholar
  3. 3.
    Venkov, B.A.: On a class of Euclidean Polyhedra. Vestn. Leningr. Univ., Ser. Mat. Fiz. 9, 11–31 (1954)MathSciNetGoogle Scholar
  4. 4.
    Voronoi, G.: Nouvelles applications des paramètres continus á la théorie des formes quadratiques Deuxiéme meḿoire: Recherches sur les paralléloédres primitifs. J. Reine Angew. Math. 134, 198–287 (1908); 136, 67–178 (1909) zbMATHGoogle Scholar
  5. 5.
    Michel, L., Ryshkov, S.S., Senechal, M.: An extension of Voronoï’s theorem on primitive parallelotopes. Europ. J. Combinatorics 16, 59–63 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dolbilin, N., Itoh, J.-I., Nara, C.: Affine equivalent classes of parallelohedra. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds.) CGGA 2010. LNCS, vol. 7033, pp. 55–60. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nikolai Dolbilin
    • 1
  • Jin-ichi Itoh
    • 2
  • Chie Nara
    • 3
  1. 1.Steklov Institute of MathematicsRussian Academy of ScienceMoscowRussia
  2. 2.Faculty of EducationKumamoto UniversityJapan
  3. 3.Liberal Arts Education Center, Aso CampusTokai UniversityAsoJapan

Personalised recommendations