Geodesic
Parallelotopes of non-zero width
Sbornik. Mathematics, Tome 195 (2004) no. 5, pp. 669-686

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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. 
@article{SM_2004_195_5_a2,
     author = {V. P. Grishukhin},
     title = {Parallelotopes of non-zero width},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {195},
     number = {5},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_5_a2/}
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V. P. Grishukhin. Parallelotopes of non-zero width. Sbornik. Mathematics, Tome 195 (2004) no. 5, pp. 669-686. http://geodesic.mathdoc.fr/item/SM_2004_195_5_a2/