The Shellability of Simplices

Abstract

Shelling can be looked at as a way of piecing together a surface ( or taking it apart), almost as if using legos. The pieces we are using are points, edges, triangles, tetrahedra, and larger n-dimensional cells. You can shell any triangulated surface. Let's begin with an example. In order to shell a triangulated disk, we begin by picking any triangle to shell. The only rule we must follow as we proceed is that the next triangle we shell must have a one dimensional intersection with the previously shelled part of the disk. Here is an example of a potential shelling o�f a triangulated disk. . . . In this paper, we will only be shelling simplices. An n-simplex is an n-dimensional cell. For example, a 0-simplex is a point, a I-simplex is an edge, a 2-simplex is a triangle, etc. In a simplex, every vertex is connected to every other vertex by an edge; every 3 edges bound a triangle; every 4 triangles bound a tetrahedron; etc. [From introductory section]