Subdivisions and Triangulations of Polytopes

Authored by: Carl W. Lee

Discrete and Computational Geometry

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:

10.1201/9781420035315.ch17

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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, …, Pm }. A subdivision is a triangulation if each Pi 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.

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