Geodesic
Properties of Faces of Parallelohedra
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 112-126

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

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. 
@article{TM_2009_266_a5,
     author = {N. P. Dolbilin},
     title = {Properties of {Faces} of {Parallelohedra}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {112--126},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_266_a5/}
}
TY  - JOUR
AU  - N. P. Dolbilin
TI  - Properties of Faces of Parallelohedra
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2009
SP  - 112
EP  - 126
VL  - 266
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2009_266_a5/
LA  - ru
ID  - TM_2009_266_a5
ER  - 
%0 Journal Article
%A N. P. Dolbilin
%T Properties of Faces of Parallelohedra
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2009
%P 112-126
%V 266
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2009_266_a5/
%G ru
%F TM_2009_266_a5
N. P. Dolbilin. Properties of Faces of Parallelohedra. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 112-126. http://geodesic.mathdoc.fr/item/TM_2009_266_a5/