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Convex polytopes. Prepared by Volker Kaibel, Victor Klee, and Günter M. Ziegler. 2nd ed. (English) Zbl 1024.52001
Graduate Texts in Mathematics. 221. New York, NY: Springer. xvi, 468 p. (2003).
The book ‘Convex polytopes’ by Branko Grünbaum (prepared with the cooperation of Victor Klee, Micha Perles, and Geoffrey C. Shephard) published in 1966 (see the extensive review and content in Zbl 0163.16603) has been a fundamental and inspiring work on the combinatorical theory of convex polytopes. Many topics, mentioned first in the book, have been taken up by the community leading to growing activities with other parts of mathematics; many conjectures have been solved.
Unfortunately, the book went out of print as early as 1970.
Inspired by the demand for the book and ‘biased by our interests’ the authors K. Kaibel, V. Klee and G. M. Ziegler present now a new (2nd) edition:
(From the Preface to the 2002 edition:) “The present new edition contains the full text of the original, in the original typesetting, and with the original page numbering – except for the table of contents and the index, which have been expanded. You will see yourself all that has been added.”
“The material that we have added provides a direct guide to more than 400 papers and books that have appeared since 1967; thus references like “Grünbaum [a]” refer to the additional bibliography which starts on page 448a. Many of those publications are themselves surveys.”
The reviewer welcomes the dear separation of the original text and the new, ‘up-dating’ text in the ‘Additional notes and comments’ bridging the gap to the present state of research. An example is the growing work on arrangements and oriented matroids today represented by Björner, Bokowski, Richter-Gebert, G. M. Ziegler and many others.
A highlight is the additional, actual bibliography which reflects areas and authors of currently dominating research fields in the combinatorial theory of convex polytopes having their stimulating basis in the ideas of Branko Grünbaum.
Read the book.
Reviewer: G.Ehrig (Berlin)

MSC:
52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry
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