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I am interested in alternatives to Ziegler's Lectures on Polytopes, which is the suggested textbook for a course I am attending. I find the conversational style of the book jarring.

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  • $\begingroup$ I would recommend Brondsted, I'm currently reading through it and it is packed with information. It is very carefully written and it seems that every sentence is carefully placed to be essential at that moment in the book. $\endgroup$ – Samuel Reid Jan 7 '12 at 23:07
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Other books on Convex Polytopes are: Arne Brondsted, An Introduction to Convex Polytopes, Branko Grünbaum, Convex Polytopes (there is a second edition that updates the 1967 version), A. D. Alexandrov, Convex Polyhedra (translation from Russian of a Russian book from 1950, but with update and notes). They all have their pros/cons. I, at least, think Ziegler's book is excellent.

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  • $\begingroup$ Grünbaum's book should be mandatory reading! $\endgroup$ – Mariano Suárez-Álvarez Nov 2 '11 at 9:36
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I think this (Regular Polytopes by Coxeter) would be a good book. I liked his book on geometry. Also the reviews seem to indicate that is is pretty good.

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Some of the topics of Ziegler's (excellent) book (e.g. Gale transforms, f-vectors, the secondary polytope, fiber polytopes) are also covered in the "Triangulations" book of De Loera, Rambau and Santos. The treatment is from a slightly different perspective and definitely worth a look. They provide many pictures.

Another alternative (also more from the triangulations perspective) is the book Lectures in Geometric Combinatorics.

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