rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Convex polytopes
  name:
    name part: Grünbaum, Branko.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    date issued: 1967
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: preservation
    reformatting quality: access
    form: remote
    extent: 1 online resource (xiv, 456 pages) : illustrations.
  abstract: "The appearance of Grnbaum'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 Grnbaum 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)
  table of contents: 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 -- 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! $$ left[ { frac{1} {2}d} right] $$-Neighborly d-polytopes -- 7.3 Exercises -- 7.4 Remarks -- 7.5 Additional notes and co…
  note: [by] Branko Grünbaum, with the cooperation of Victor Klee, M.A. Perles, and G.C. Shephard.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (pages 429-448).
  subject:
    topic: Convex polytopes
  subject:
    topic: Convex polytopes
  subject:
    topic: Konvexes Polytop
  subject:
    topic: Konvexität
  classification: QA482 .G7
  classification: 513/.5
  classification: 31.50
  classification: SK 300
  classification: SK 380
  related item:
    title info:
      title: Convex polytopes
    name:
      name part: Grünbaum, Branko.
    origin info:
      publisher: London, New York Interscience [1967
    identifier: (DLC) 67020423
    identifier: (OCoLC)528820
  related item:
    title info:
      title: Pure and applied mathematics (Interscience Publishers) ; v. 16
  identifier: 9781461300199 (electronic bk.)
  identifier: 1461300193 (electronic bk.)
  identifier: 0387404090
  identifier: 9780387404097
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCLCE
    record creation date: 111008
    record change date: 20260422204744.9
    record identifier: in00003548027
    language of cataloging:
      language term: eng