Geodesic
A Definition of Type Domain of a Parallelotope
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 6, pp. 129-134.

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Each convex polytope $P=P(\alpha)$ can be described by a set of linear inequalities determined by vectors $p$ and right hand sides $\alpha(p)$. For a fixed set of vectors $p$, a type domain ${\mathcal D}(P_0)$ of a polytope $P_0$ and, in particular, of a parallelotope $P_0$ is defined as a set of parameters $\alpha(p)$ such that polytopes $P(\alpha)$ have the same combinatorial type as $P_0$ for all $\alpha\in{\mathcal D}(P_0)$. In the second part of the paper, a facet description of zonotopes and zonotopal parallelotopes are given. The article is published in the author's wording.
Keywords: parallelotope, zonotope.
Mots-clés : type domain 
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V. P. Grishukhin. A Definition of Type Domain of a Parallelotope. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 6, pp. 129-134. http://geodesic.mathdoc.fr/item/MAIS_2013_20_6_a10/

[1] G. F. Voronoi, “Nouvelles applications de paramètres continus á la théorie de forms quadratiques, Deuxième memoire”, J. reine angew. Math., 134 (1908), 198–287 ; 136 (1909), 67–178 | Zbl | Zbl

[2] M. Aigner, Combinatorial Theory, Springer-Verlag, 1979 | MR | Zbl

[3] M. Deza, V. Grishukhin, “Voronoi's conjecture and space tiling zonotopes”, Mathematika, 51, 1–10 | MR

[4] M. Deza, V. Grishukhin, “Properties of parallelotopes equivalent to Voronoi's conjecture”, Europ. J. Combinatorics, 25 (2004), 517–533 | DOI | MR | Zbl

[5] N. P. Dolbilin, “Properties of faces of parallelohedra”, Proc. Steklov Inst. of Math., 266, 2009, 112–126 | DOI | MR | Zbl

[6] R. M. Erdahl, “Zonotopes, Dicings, and Voronoi's conjecture on Parallelohedra”, Eur. J. Combin., 20 (1999), 527–549 | DOI | MR | Zbl

[7] A. Björner, M. Las Vergnas, B. Sturmfels, N. White, G.H. Ziegler, Oriented Matroids, Encyclopedia of Mathematics and its Applications, 46, Cambridge Univ. Press, 1999 | MR | Zbl