Triangulations - Jesus De Loera - Bog

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.