BASIC PROPERTIES OF CONVEX POLYTOPES

BASIC PROPERTIES OF CONVEX POLYTOPES (1997)

Cached

Download Links

by Martin Henk , Jürgen Richter-Gebert , Günter M. Ziegler

Citations:

BibTeX

@MISC{Henk97basicproperties,
    author = {Martin Henk and Jürgen Richter-Gebert and Günter M. Ziegler},
    title = { BASIC PROPERTIES OF CONVEX POLYTOPES},
    year = {1997}
}

Bookmark

OpenURL

Abstract

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical subjects, ranging from integration theory, algebraic topology, and algebraic geometry (toric varieties) to linear and combinatorial

Citations

432	Convex Bodies: The Brunn–Minkowski Theory - Schneider - 1993
156	Lectures on polytopes, Graduate Texts in Mathematics, vol. 152 - Ziegler - 1995
96	Vorlesungen über Inhalt, Oberfläche und Isoperimetrie - Hadwiger - 1957
74	An elementary introduction to modern convex geometry - Ball - 1997
71	polymake: a Framework for Analyzing Convex Polytopes and Simplicial Complexes. http://www.math.tu-berlin. de/polymake - Gawrilow, Joswig - 1997
67	Vorlesungen uber die Theorie der Polyeder - Steinitz, Rademacher - 1934
44	Geometry of Cuts and Metrics, volume 15 of Algorithms and Combinatorics - Deza, Laurent - 1997
40	Convex polytopes, Interscience - Grünbaum - 1967
38	Valuations and dissections. Handbook of convex geometry - McMullen - 1993
37	a POlyhedron Representation Transformation Algorithm, version 1.3.2 - Christof, PORTA - 1999
33	Polyhedral theory - Grötschel, Padberg - 1985
30	A counterexample to Borsuk's conjecture - Kahn, Kalai - 1993
24	Combinatorial aspects of convex polytopes, Handbook of convex geometry - Bayer, Lee - 1993
23	Non-linear angle-sum relations for polyhedral cones and polytopes - McMullen - 1975
23	On puzzles and polytope isomorphisms - Blind, Mani-Levitska - 1987
22	On the graph structure of convex polyhedra in n-space - Balinski - 1961
20	Random projections of regular simplices - Affentranger, Schneider - 1992
14	Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem - Vershik, Sporyshev - 1992
13	Mixed volumes of polytopes - Betke - 1992
13	Valuations and dissections - McMullen - 1993
13	Lectures on 0/1-polytopes - Ziegler - 1997
12	On 0 − 1 polytopes with many facets - Bárány, Pór
12	Realization Spaces of Polytopes. Volume 1643 - Richter-Gebert
11	On combinatorial and affine automorphisms of polytopes - BOKOWSKI, EWALD, et al. - 1984
9	Random projections of regular polytopes - Henk - 1999
9	A quantitative Steinitz’ theorem, Beiträge zur Algebra und Geometrie 35 - ONN, STURMFELS - 1994
8	Neighborly polytopes - Shemer - 1982
7	Zonotopal tilings and the Bohne-Dress theorem - Richter-Gebert, Ziegler - 1994
6	Intrinsic volumes and lattice points of crosspolytopes - Betke, Henk - 1993
6	Theorie der konvexen Körper. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 3, Heft 1 - Bonnesen, Fenchel - 1934
6	Cut Polyhedra and Metrics - Deza, Laurent - 1996
6	Regular simplices and Gaussian samples - Baryshnikov, Vitale - 1994
5	Gitterpunktanzahl im Simplex und Wills’sche Vermutung - Hadwiger - 1979
5	Mixed volumes - Sangwine-Yager - 1993
4	Regular simplices and Gaussian samples. Discrete Comput - Baryshnikov, Vitale - 1994
4	Duality, sections and projections of certain Euclidean tilings - McMullen - 1994
4	A quantitative Steinitz’ theorem - Onn, Sturmfels - 1994
4	Convex: the Brunn-Minkowski theory - Schneider - 1993
3	Random projections of regular simplices, Discrete Comput. Geometry 7 - Affentranger - 1992
2	The number of faces of centrally-symmetric polytopes (Research Problem - Kalai - 1989
2	Realization Spaces of 4-Polytopes are Universal. Habilitationsschrift, Techniche Universitat - Richter-Gebert - 1995
2	Zonotopal tilings and the Bohne-Dress theorem, in: "Jerusalem Combinatorics '93 - Ziegler - 1994
2	Sangwine-Yager: Mixed volumes, Handbook of Convex Geometry - R - 1993
2	Computational Synthetic Geometry. Volume 1355 - Bokowski, Sturmfels - 1989
2	Polyhedral complexes and their relatives - Klee, Kleinschmidt - 1995
2	Every simplicial polytope with at most d+4 vertices is a quotient of a neighborly polytope - Kortenkamp - 1997
2	Gram’s equation – a probabilistic proof - Welzl - 1994
1	On the distribution of order types - Bokowski, Richter-Gebert, et al. - 1992
1	otschel & M. Padberg: Polyhedral Theory, Chapter 8 in: "The Traveling Salesman Problem - Gr - 1985
1	unbaum: Convex Polytopes, Interscience, London 1967; revised edition - Gr