Cone decompositions of non-simple polytopes

J.A. Agapito, Leonor Godinho

Type: Article

Publication Date: 2016-01-01

Citations: 2

DOI: https://doi.org/10.4310/jsg.2016.v14.n3.a4

Abstract

A polytope cone decomposition expresses the characteristic function of a polytope as a sum of characteristic functions of convex cones associated to its faces.In this work we generalize the decompositions for simple polytopes introduced in [3] to any convex polytope.

Locations

Journal of Symplectic Geometry - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Simple Extensions of Polytopes	2014	Volker Kaibel Matthias Walter
+ PDF Chat	Simple extensions of polytopes	2015	Volker Kaibel Matthias Walter
+	Polytopes	2015	Henriette Elvang Yu-tin Huang
+	Polytopes	2015	Chris Godsil Karen Meagher
+	Truncations of simple polytopes and applications	2015	Victor Matveevich Buchstaber Nikolai Erokhovets
+	Combinatorial Aspects of Convex Polytopes	1993	Margaret M. Bayer Carl W. Lee
+	Centric decomposition of polytopes	1903	P. H. Schoute
+	A CLASS OF SYMMETRIC POLYTOPES	1989	A. HILL D.G. LARMAN
+	A class of symmetric polytopes	1989	Anthony Hill D. G. Larman
+ PDF Chat	Approximate cone factorizations and lifts of polytopes	2014	João Gouveia Pablo A. Parrilo Rekha R. Thomas
+	Polytopes	2010	Corrado De Concini Claudio Procesi
+	Representations of polytopes	2011	Michael Gene Dobbins
+	Complete descriptions of small multicut polytopes	1991	Michel Deza Martin Grötschel Monique Laurent
+	Revealing properties of regular convex polytopes in negative dimensions	2023
+	Nondegenerate families of convex cones and convex polytopes	1979	Meir Katchalski
+	Geometry and combinatorics of polytopes	2015	Victor Matveevich Buchstaber Taras Panov
+	Addition and decomposition of convex polytopes	1964	William J. Firey Branko Grünbaum
+	Flat regular polytopes	1997	Peter McMullen Egon Schulte
+	Regular Polytopes	1964	Michael E. Goldberg H. S. M. Coxeter
+	Regular Polytopes	1976	Magnus J. Wenninger H. S. M. Coxeter

Works That Cite This (2)

Action	Title	Year	Authors
+ PDF Chat	Approximating sums by integrals only: multiple sums and sums over lattice polytopes	2022	Iosif Pinelis
+	Approximating sums by integrals only: multiple sums and sums over lattice polytopes	2017	Iosif Pinelis

Works Cited by This (10)

Action	Title	Year	Authors
+ PDF Chat	Polar decomposition and Brion’s theorem	2005	Christian Haase
+	A weighted version of quantization commutes with reduction for a toric manifold	2005	J.A. Agapito
+ PDF Chat	Euler-Maclaurin with remainder for a simple integral polytope	2005	Yael Karshon Shlomo Sternberg Jonathan Weitsman
+ PDF Chat	Localization for equivariant cohomology with varying polarization	2012	Megumi Harada Yael Karshon
+	New polytope decompositions and Euler–Maclaurin formulas for simple integral polytopes	2007	J.A. Agapito Leonor Godinho
+ PDF Chat	The weighted Euler-Maclaurin formula for a simple integral polytope	2005	J.A. Agapito Jonathan Weitsman
+ PDF Chat	Toric symplectic singular spaces I: isolated singularities	2005	D. Burns Victor Guillemin Eugene Lerman
+ PDF Chat	Weighted Brianchon-Gram Decomposition	2006	J.A. Agapito
+ PDF Chat	GEOMETRIC SPACES FROM ARBITRARY CONVEX POLYTOPES	2011	Fiammetta Battaglia
+ PDF Chat	Polytope Volume Computation	1991	Jim Lawrence