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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 266, Pages 112–126 (Mi tm1869)  
This article is cited in 18 scientific papers (total in 18 papers)

Properties of Faces of Parallelohedra

N. P. Dolbilin

Steklov Institute of Mathematics, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (258 kB) Citations (18)
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Abstract: We consider an important class of polytopes, called parallelohedra, that tile the Euclidean space. The concepts of a standard face of a parallelohedron and of the index of a face are introduced. It is shown that the sum of indices of standard faces in a parallelohedron is an invariant; this implies the Minkowski bound for the number of facets of parallelohedra. New properties of faces of parallelohedra are obtained.
Received in March 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 266, Pages 105–119
DOI: https://doi.org/10.1134/S0081543809030067
Bibliographic databases:
Document Type: Article
UDC: 511.9+514.1
Language: Russian
Citation: N. P. Dolbilin, “Properties of Faces of Parallelohedra”, Geometry, topology, and mathematical physics. II, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 112–126; Proc. Steklov Inst. Math., 266 (2009), 105–119
Citation in format AMSBIB
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\paper Properties of Faces of Parallelohedra
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\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
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\pages 112--126
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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