Polytopes: Abstract, Convex and ComputationalTibor Bisztriczky, Peter McMullen, Rolf Schneider, Asia Ivic Weiss Springer Science & Business Media, 2012年12月6日 - 507 頁 The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels. |
內容
H S M Coxeter The evolution of CoxeterDynkin diagrams 21 | 43 |
H Martini A hierarchical classification of Euclidean polytopes | 71 |
P McMullen Modern developments in regular polytopes | 97 |
E Schulte Classification of locally toroidal regular polytopes | 125 |
Gruber Approximation by convex polytopes | 173 |
G Kalai Some aspects of the combinatorial theory of convex polytopes 205 | 231 |
W Kühnel Manifolds in the skeletons of convex polytopes | 240 |
W Lee Generalized stress and motions | 249 |
R Schneider Polytopes and BrunnMinkowski theory 273 | 301 |
J Bokowski On recent progress in computational synthetic geometry 335 | 359 |
P Gritzmann and V Klee On the complexity of some basic problems | 373 |
P Kleinschmidt The diameter of polytopes and related applications | 467 |
J Schaer editor Contributed problems | 493 |
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常見字詞
abstract abstract polytope abstract regular polytopes affine algebra algorithm anticuts approximation asymptotic automorphism C-group called cell chiral coefficients Cohen-Macaulay combinatorial conjecture construction contains convex bodies convex polytopes corresponding Coxeter groups cube d-polytope defined denote diagram dimension dual edges equivalent Euclidean Eulerian poset example face lattice finite flag vectors formula function g-theorem Geom geometry given graph Gruber Grünbaum h-vector hence hyperplane inequalities integer intersection isogonal isomorphic k-stress Kalai Lemma linear locally toroidal Math Mathematics matroid polytope McMullen metric polytope mixed volumes nodes nonnegative number of faces obtained oriented matroid P₁ pair points polygons polyhedron polynomial problem proof rank rational realization regular polytopes result Schulte sequence simplex simplicial complex simplicial polytopes space spheres spherical Stanley subdivision subgroup subset symmetry group Theorem theory topological toroidal triangle facets triangulation vertex figure volume computation zonotope