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Zipper Foldings of a Diamond

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Kyle Sykes, Saint Louis University

What
  • Topology Seminar
When Tue, Oct 15, 2013
from 02:00 PM to 03:00 PM
Where Ritter Hall 223
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Abstract:

 

A folding of a polygon is a gluing of the points on the perimeter together to form a polyhedron.  We will examine a particular type of folding known as the zipper folding where the perimeter of the polygon is identified starting from a specified point gluing together points equidistant from the starting point (as measured along the perimeter), which “zips” up the boundary of the polygon into a polyhedron.  We classify and compute the combinatorially distinct convex foldings of a diamond shape which are obtained via a zipper folding along the boundary of the shape. In the process, we explore computational aspects of this problem; in particular, we outline several useful techniques for computing both the edge set of the final polyhedron and its three-dimensional coordinates.

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