Triangulations

Triangulations appear everywhere, from volume computations and meshing

to algebra and topology. This book studies the subdivisions and

triangulations of polyhedral regions and point sets and presents the

first comprehensive treatment of the theory of secondary polytopes and

related topics.

A central theme of the book is the use of the rich structure of the

space of triangulations to solve computational problems (e.g., counting

the number of triangulations or finding optimal triangulations with

respect to various criteria), and to establish connections to

applications in algebra, computer science, combinatorics, and

optimization.

With many examples and exercises, and with nearly five hundred

illustrations, the book gently guides readers through the properties

of the spaces of triangulations of "structured" (e.g., cubes, cyclic

polytopes, lattice polytopes) and "pathological" (e.g., disconnected

spaces of triangulations) situations using only elementary principles.