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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. $\endgroup$ Jan 7, 2012 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! $\endgroup$ Nov 2, 2011 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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  • $\begingroup$ Here is my opinion: yes, it is a good book, but its goal is very distinct from the one of Ziegler' book. Coxeter's book is focused on the highly symmetric polytopes (so to say, the exceptions), while Ziegler (and also Grünbaum) is more about the "generic polytope" and general structure. You can't really substitute one by the other. And also, the style of Coxeter's book is the style of its time (e.g quite some trigonometry), where I would claim that Ziegler appeals more to the mathematician of the 21st century. $\endgroup$
    – M. Winter
    Aug 9, 2020 at 8:40
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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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