By Rekha R. Thomas

This booklet offers a direction within the geometry of convex polytopes in arbitrary size, appropriate for a complicated undergraduate or starting graduate pupil. The publication begins with the fundamentals of polytope idea. Schlegel and Gale diagrams are brought as geometric instruments to imagine polytopes in excessive measurement and to unearth strange phenomena in polytopes. the guts of the publication is a remedy of the secondary polytope of some degree configuration and its connections to the country polytope of the toric perfect outlined by means of the configuration. those polytopes are fairly fresh constructs with various connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections depend on Gröbner bases of toric beliefs and different equipment from commutative algebra. The ebook is self-contained and doesn't require any historical past past simple linear algebra. With a variety of figures and workouts, it may be used as a textbook for classes on geometric, combinatorial, and computational elements of the idea of polytopes.