By Rekha R. Thomas
This e-book offers a path within the geometry of convex polytopes in arbitrary size, compatible for a complicated undergraduate or starting graduate pupil. The booklet starts off with the fundamentals of polytope thought. Schlegel and Gale diagrams are brought as geometric instruments to imagine polytopes in excessive measurement and to unearth weird and wonderful phenomena in polytopes. the center of the booklet is a therapy of the secondary polytope of some degree configuration and its connections to the country polytope of the toric excellent outlined by way of the configuration. those polytopes are quite fresh constructs with a variety of connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections depend upon Gröbner bases of toric beliefs and different equipment from commutative algebra. The e-book is self-contained and doesn't require any historical past past easy linear algebra. With quite a few figures and workouts, it may be used as a textbook for classes on geometric, combinatorial, and computational points of the idea of polytopes.