Document Type
Article
Publication Date
1-1-2015
Publication Title
Russian Mathematical Surveys
Abstract
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.
Keywords
Coloured polygon, Maxwell polytope, McMullen's polytope algebra, Minkowski difference, Polytopal function, Stressed graph, Support functions
Volume
70
Issue
6
First Page
1105
Last Page
1165
DOI
10.1070/RM2015v070n06ABEH004975
ISSN
00360279
Rights
© the authors, 2015
Recommended Citation
Yu Panina, G. and Streinu, I., "Virtual Polytopes" (2015). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/277
Comments
Peer reviewed accepted manuscript.