Affine Equivalent Classes of Parallelohedra

  • Nikolai Dolbilin
  • Jin-ichi Itoh
  • Chie Nara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


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.


Uniqueness Theorem Combinatorial Type Equivalent Classis Hexagonal Prism Rhombic Dodecahedron 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nikolai Dolbilin
    • 1
  • Jin-ichi Itoh
    • 2
  • Chie Nara
    • 3
  1. 1.Institute of MathematicsRussian Academy of ScienceMoscowRussia
  2. 2.Faculty of EducationKumamoto UniversityJapan
  3. 3.Liberal Arts Education CenterAso Campus, Tokai UniversityAsoJapan

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