This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.

Autorentext

A.D. Alexandrov was awarded the Stalin State Prize in 1942, the Lobachevsky prize in 1952, and the Euler Golden Medal in 1992.

Zusammenfassung

Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to a polyhedron, e.g. the lengths of edges, areas of faces, etc. This vital and clearly written book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. It is a wonderful source of ideas for students.

The English edition includes numerous comments as well as added material and a comprehensive bibliography by V.A. Zalgaller to bring the work up to date. Moreover, related papers by L.A.Shor and Yu.A.Volkov have been added as supplements to this book.

Inhalt
Basic Concepts and Simplest Properties of Convex Polyhedra.- Methods and Results.- Uniqueness of Polyhedra with Prescribed Development.- Existence of Polyhedra with Prescribed Development.- Gluing and Flexing Polyhedra with Boundary.- Congruence Conditions for Polyhedra with Parallel Faces.- Existence Theorems for Polyhedra with Prescribed Face Directions.- Relationship Between the Congruence Condition for Polyhedra with Parallel Faces and Other Problems.- Polyhedra with Vertices on Prescribed Rays.- Infinitesimal Rigidity of Convex Polyhedra with Stationary Development.- Infinitesimal Rigidity Conditions for Polyhedra with Prescribed Face Directions.- Supplements.