Abstract.
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.
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Karpenkov, O. Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions. Mh Math 152, 217–249 (2007). https://doi.org/10.1007/s00605-007-0478-0
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DOI: https://doi.org/10.1007/s00605-007-0478-0