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This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.
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Convex polytopes --- Symmetry --- Polytopes convexes --- Symétrie --- Symétrie --- Geometrie --- Polyedres
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Geometry --- Convex polytopes --- Géométrie --- Polytopes convexes --- Géométrie
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"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London).
Convex polytopes --- Polytopes convexes --- Convex polytopes. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Convex geometry . --- Discrete geometry. --- Convex and Discrete Geometry. --- Discrete mathematics --- Combinatorial geometry
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Geometry --- Convex polytopes --- Géométrie. --- Polytopes convexes --- Convex geometry --- Polyhedra --- Géométrie convexe. --- Polyèdres.
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Geometry --- Convex polytopes --- Polytopes convexes --- Convex geometry --- Polyhedra --- Géométrie convexe --- Polyèdres --- Géométrie --- Géométrie convexe --- Polyèdres --- Géométrie
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Polytopes --- Combinatorial optimization --- Polyhedra --- #TELE:SISTA --- Hyperspace --- Topology --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization --- Geometry --- Convex polytopes --- Géométrie --- Polytopes convexes
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Convex geometry --- Polyhedra --- Géométrie convexe --- Polyèdres --- Geometry --- Convex polytopes --- Géométrie --- Polytopes convexes --- Géométrie convexe --- Polyèdres --- Géométrie
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Convex geometry --- Polyhedra --- Géométrie convexe. --- Polyèdres. --- Geometry --- Convex polytopes --- Géométrie. --- Polytopes convexes --- Choquet, Théorie de. --- Choquet theory --- Inequalities (Mathematics) --- Inégalités (mathématiques)
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Convex geometry --- Polyhedra --- Géométrie convexe --- Polyèdres --- Geometry --- Convex polytopes --- Géométrie --- Polytopes convexes --- Géométrie convexe --- Polyèdres --- Géométrie
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