
Preface  Preview Material  Table of Contents 
Student Mathematical Library 2006; 143 pp; softcover Volume: 33 ISBN10: 0821841408 ISBN13: 9780821841402 List Price: US$30 Member Price: US$24 Order Code: STML/33 See also: Configurations of Points and Lines  Branko Grunbaum Toric Varieties  David A Cox, John B Little and Henry K Schenck  This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gröbner bases of toric ideals and other methods from commutative algebra. The book is selfcontained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes. This book is published in cooperation with IAS/Park City Mathematics Institute. Readership Undergraduate and graduate students interested in computational geometry and polytopes. Reviews "Undergraduates will find this a very friendly and stimulating introduction to creative mathematics in higher dimensions."  CHOICE Magazine 


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