related to Cauchy's theorem that polyhedra with flat faces form rigid structures, and describing the differences between the rigidity and infinitesimal rigidity of polyhedra, as developed analogously to Cauchy's rigidity theorem by Max Dehn. The 2005 English edition adds comments and bibliographic information regarding many problems that were posed as open in the 1950 edition but subsequently solved. It also includes in a chapter of supplementary material the translations of three related articles by Volkov and Shor, including a simplified proof of Pogorelov's theorems generalizing Alexandrov's uniqueness theorem to non-polyhedral convex surfaces. Audience and reception Robert Connelly writes that, for a work describing significant developments in the theory of convex polyhedra that was however hard to access in the west, the English translation of Convex Polyhedra was long overdue. He calls the material on Alexandrov's uniqueness theorem "the star result in the book", and he writes that the book "had a great influence on countless Russian mathematicians". Nevertheless, he complains about the book's small number of exercises, and about an inconsistent level presentation that fails to distinguish important and basic results from specialized technicalities. Although intended for a broad mathematical audience, Convex Polyhedra assumes a significant level of background knowledge in material including topology, differential geometry, and linear algebra. Reviewer Vasyl Gorkaviy recommends Convex Polyhedra to students and professional mathematicians as an introduction to the mathematics of convex polyhedra. He also writes that, over 50 years after its original publication, "it still remains of great interest for specialists", after being updated to include many new developments and to list new open problems in the area. See also List of books about polyhedra References Polyhedra Mathematics books 1950 non-fiction books 2005 non-fiction books