Acute triangulations of polyhedra and the Euclidean space
Proceedings of the twenty-sixth annual symposium on Computational geometry
On the facets of the secondary polytope
Journal of Combinatorial Theory Series A
Counting plane graphs: flippability and its applications
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Applying ACL2 to the formalization of algebraic topology: simplicial polynomials
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
On a linear program for minimum-weight triangulation
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An output-sensitive algorithm for computing projections of resultant polytopes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Formalization of a normalization theorem in simplicial topology
Annals of Mathematics and Artificial Intelligence
There are only two nonobtuse binary triangulations of the unit n-cube
Computational Geometry: Theory and Applications
A simple aggregative algorithm for counting triangulations of planar point sets and related problems
Proceedings of the twenty-ninth annual symposium on Computational geometry
Combinatorics of 4-dimensional resultant polytopes
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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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.