Geodesic
The average number of vertexes of Klein polyhedrons for integer lattices
Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 48-55

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Low estimate for the average number for vertices of Klein polyhedron of integer lattices with given determinant is derived. The low estimate coincides with the high estimate up to a constant. The constant depends on dimension of lattices. High-low estimates for the number of relative minima of integer lattices with given determinant is derived from this fact. 
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     author = {A. A. Illarionov and D. Slinkin},
     title = {The average number of vertexes of {Klein} polyhedrons for integer lattices},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     number = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a4/}
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A. A. Illarionov; D. Slinkin. The average number of vertexes of Klein polyhedrons for integer lattices. Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 48-55. http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a4/