Branko Grünbaum was awarded the 2005 AMS Leroy P. Steele Prize for Mathematical Exposition. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics.
Grünbaum was honored for his book, Convex Polytopes. The prize citation states: "[This book] has served both as a standard reference and as an inspiration for three and a half decades of research in the theory of polytopes. That theory is currently very active and enjoys connections with many other areas of mathematics, including optimization, computational algebra, algebraic geometry, and representation theory. Much of the development that led to the present, thriving state of polytope theory owes its existence to this book, which served as a source of information for workers in the field and as a source of inspiration for them to enter the field. Despite the passage of time, Convex Polytopes retains its value both as an exposition of the theory and as a reference work. Springer-Verlag's decision to issue a second edition in 2003, consisting of Grünbaum's original text plus notes by Volker Kaibel, Victor Klee, and Guenter Ziegler to describe newer developments, will extend the book's influence to future generations of mathematicians."