Geodesic
Parallelohedra defined by quadratic forms
Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 95-108

Voir la notice de l'article provenant de la source Math-Net.Ru

The results of Section III of G. F. Voronoi's famous memoir are presented in modern terms. The description of a parallelohedron by a system of linear constraints with quadratic right-hand side naturally leads to the notion of a contact face, which is called a standard face by N. P. Dolbilin. It is proved that a nonempty intersection of two contact faces generates a $4$- or $6$-belt of these contact faces. As an example, zonotopes defined by quadratic forms are considered. In particular, zonotopal parallelohedra of Voronoi's principal domain are examined in detail. It is shown that these parallelohedra are submodular polytopes, which are frequently encountered in combinatorial theory. 
@article{TRSPY_2015_288_a5,
     author = {V. P. Grishukhin},
     title = {Parallelohedra defined by quadratic forms},
     journal = {Informatics and Automation},
     pages = {95--108},
     publisher = {mathdoc},
     volume = {288},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a5/}
}
TY  - JOUR
AU  - V. P. Grishukhin
TI  - Parallelohedra defined by quadratic forms
JO  - Informatics and Automation
PY  - 2015
SP  - 95
EP  - 108
VL  - 288
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a5/
LA  - ru
ID  - TRSPY_2015_288_a5
ER  - 
%0 Journal Article
%A V. P. Grishukhin
%T Parallelohedra defined by quadratic forms
%J Informatics and Automation
%D 2015
%P 95-108
%V 288
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a5/
%G ru
%F TRSPY_2015_288_a5
V. P. Grishukhin. Parallelohedra defined by quadratic forms. Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 95-108. http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a5/