Abstract

Starting from a given finite set of points V in ? d , we consider subdivisions of the convex hull of V into polytopes {P ₁, …, P_m }. A subdivision is a triangulation if each P_i is a simplex. We start with definitions and properties, then turn to methods of constructing subdivisions and triangulations, face-counting results, some particular triangulations, and secondary and fiber polytopes. We confine ourselves to triangulations of convex structures for the most part.