Geodesic
Virtual polytopes
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 6, pp. 1105-1165 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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