Geodesic
Virtual polytopes
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 6, pp. 1105-1165

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

Originating in diverse branches of mathematics, from polytope algebra and toric varieties to the theory of stressed graphs, virtual polytopes represent a natural algebraic generalization of convex polytopes. Introduced as elements of the Grothendieck group associated to the semigroup of convex polytopes, they admit a variety of geometrizations. The present survey connects the theory of virtual polytopes with other geometrical subjects, describes a series of geometrizations together with relations between them, and gives a selection of applications. Bibliography: 50 titles.
Keywords: Minkowski difference, coloured polygon, polytopal function, support functions, stressed graph, McMullen's polytope algebra, Maxwell polytope. 
@article{RM_2015_70_6_a3,
     author = {G. Yu. Panina and I. Streinu},
     title = {Virtual polytopes},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1105--1165},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2015_70_6_a3/}
}
TY  - JOUR
AU  - G. Yu. Panina
AU  - I. Streinu
TI  - Virtual polytopes
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2015
SP  - 1105
EP  - 1165
VL  - 70
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2015_70_6_a3/
LA  - en
ID  - RM_2015_70_6_a3
ER  - 
%0 Journal Article
%A G. Yu. Panina
%A I. Streinu
%T Virtual polytopes
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2015
%P 1105-1165
%V 70
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2015_70_6_a3/
%G en
%F RM_2015_70_6_a3
G. Yu. Panina; I. Streinu. Virtual polytopes. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 6, pp. 1105-1165. http://geodesic.mathdoc.fr/item/RM_2015_70_6_a3/