Monatshefte für Mathematik

, Volume 152, Issue 3, pp 217–249 | Cite as

Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

  • O. N. Karpenkov
Open Access


In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.

2000 Mathematics Subject Classification: 11H06, 52C07 
Key words: Convex polygons, integer lattices, multidimensional continued fractions 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • O. N. Karpenkov
    • 1
  1. 1.Leiden UniversityLeidenThe Netherlands

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