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Sbornik: Mathematics, 2004, Volume 195, Issue 5, Pages 669–686
DOI: https://doi.org/10.1070/SM2004v195n05ABEH000821 (Mi sm821) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Parallelotopes of non-zero width

V. P. Grishukhin

Central Economics and Mathematics Institute, RAS
English version PDF (244 kB) Citations (11)
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DOI: https://doi.org/10.1070/SM2004v195n05ABEH000821
Abstract: In 1959, Venkov introduced a concept of polytope of non-zero width in the direction of a subspace and studied parallelotopes of non-zero width. In the present paper properties of a parallelotope of non-zero width in the direction of a straight line are investigated. In particular, it is proved that a parallelotope of non-zero width in the direction of a straight line is the Minkowski sum of a parallelotope of width zero and a segment of this line. Necessary and sufficient conditions ensuring that the sum of a parallelotope and a line segment is again a parallelotope are presented.
Received: 20.03.2003
Russian version:
Matematicheskii Sbornik, 2004, Volume 195, Number 5, Pages 59–78
DOI: https://doi.org/10.4213/sm821
Bibliographic databases:
UDC: 511.9
MSC: Primary 52B11; Secondary 52C22
Language: English
Original paper language: Russian
Citation: V. P. Grishukhin, “Parallelotopes of non-zero width”, Mat. Sb., 195:5 (2004), 59–78; Sb. Math., 195:5 (2004), 669–686
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:6
    References:82
    First page:2
     
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