Lectures on Polytopes

• and Examples.- Polytopes, Polyhedra, and Cones.- Faces of Polytopes.- Graphs of Polytopes.- Steinitz’ Theorem for 3-Polytopes.- Schlegel Diagrams for 4-Polytopes.- Duality, Gale Diagrams, and Applications.- Fans, Arrangements, Zonotopes, and Tilings.- Shellability and the Upper Bound Theorem.- Fiber Polytopes, and Beyond.- Fiber Polytopes, and Beyond.

From the reviews: "This is an excellent book on convex polytopes written by a young and extremely active researcher." (Acta Scientiarum Mathematicarum) "From the publication of the first printing, in 1994, this book became one of the most widely used textbooks in Discrete Geometry. The reviewer sees at least two reasons for that: the beautiful mathematics presented here, and the fact that the book can be used at a wide variety of levels, for several different courses. ... It is not only students who can benefits from the book. Researchers will find its updates notes and references very helpful." (Miklos Bona, MathDL, August, 2007)