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140122 ||| eng |
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|a 9781461300199
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| 100 |
1 |
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|a Grünbaum, Branko
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| 245 |
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|a Convex Polytopes
|h Elektronische Ressource
|c by Branko Grünbaum ; edited by Günter M. Ziegler
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| 250 |
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|a 2nd ed. 2003
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| 260 |
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|a New York, NY
|b Springer New York
|c 2003, 2003
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| 300 |
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|a XVI, 471 p
|b online resource
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| 505 |
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|a 1 Notation and prerequisites -- 1.1 Algebra -- 1.2 Topology -- 1.3 Additional notes and comments -- 2 Convex sets -- 2.1 Definition and elementary properties -- 2.2 Support and separation -- 2.3 Convex hulls -- 2.4 Extreme and exposed points; faces and poonems -- 2.5 Unbounded convex sets -- 2.6 Polyhedral sets -- 2.7 Remarks -- 2.8 Additional notes and comments -- 3 Polytopes -- 3.1 Definition and fundamental properties -- 3.2 Combinatorial types of polytopes; complexes -- 3.3 Diagrams and Schlegel diagrams -- 3.4 Duality of polytopes -- 3.5 Remarks -- 3.6 Additional notes and comments -- 4 Examples -- 4.1 The d-simplex -- 4.2 Pyramids -- 4.3 Bipyramids -- 4.4 Prisms -- 4.5 Simplicial and simple polytopes -- 4.6 Cubical polytopes -- 4.7 Cyclic polytopes -- 4.8 Exercises -- 4.9 Additional notes and comments -- 5 Fundamental properties and constructions -- 5.1 Representations of polytopes as sections or projections -- 5.2 The inductive construction of polytopes --
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| 505 |
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|a 5.3 Lower semicontinuity of the functions fk(P) -- 5.4 Gale-transforms and Gale-diagrams -- 5.5 Existence of combinatorial types -- 5.6 Additional notes and comments -- 6 Polytopes with few vertices -- 6.1 d-Polytopes with d + 2 vertices -- 6.2 d-Polytopes with d + 3 vertices -- 6.3 Gale diagrams of polytopes with few vertices -- 6.4 Centrally symmetric polytopes -- 6.5 Exercises -- 6.6 Remarks -- 6.7 Additional notes and comments -- 7 Neighborly polytopes -- 7.1 Definition and general properties -- 7.2 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG % aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga % aiaawUfacaGLDbaaaaa!40CC!
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| 653 |
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|a Convex geometry
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| 653 |
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|a Convex and Discrete Geometry
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| 653 |
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|a Discrete geometry
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| 700 |
1 |
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|a Ziegler, Günter M.
|e [editor]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Graduate Texts in Mathematics
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| 028 |
5 |
0 |
|a 10.1007/978-1-4613-0019-9
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4613-0019-9?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 516
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| 520 |
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|a "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)
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