December 2012
Intermediate to advanced
631 pages
13h 10m
English
Doug Moore, Rice University, Houston, Texas
It is not well-known that simplices can be divided into subsimplices just as boxes can be divided into subboxes. This chapter presents two methods for dividing an n-simplex into 2n simplices and discusses some applications of the subdivision of simplices. The generalization of a triangle or tetrahedron to any dimension is a simplex, which is defined as the convex hull of an affinely independent point set. The structure of a simplex is such that any pair of its vertices form an edge, any three of its vertices form a face, any four of its vertices form a cell, and so on. A simplex is the simplest kind of polytope. The chapter describes how a uniform ...
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