Russian Mathematical Surveys
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.
Coloured polygon, Maxwell polytope, McMullen's polytope algebra, Minkowski difference, Polytopal function, Stressed graph, Support functions
© the authors, 2015
Yu Panina, G. and Streinu, I., "Virtual Polytopes" (2015). Computer Science: Faculty Publications, Smith College, Northampton, MA.