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The zipper
foldings of the diamond
Erin W. Chambers, Di Fang, Kyle A. Sykes, Cynthia M. Traub and Philip Trettenero
Vol. 8 (2015), No. 3, 521–534
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Abstract |
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In this paper, we classify and compute the convex foldings of a particular rhombus that 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. We partition the set of possible zipper starting points into subintervals representing equivalence classes induced by these edge sets. In addition, we explore nonconvex foldings of this shape which are obtained by using a zipper starting point outside of the interval corresponding to a set of edges where the polygon folds to a convex polyhedron; surprisingly, this results in multiple families of nonconvex and easily computable polyhedra. |
Keywords
computational geometry, folding algorithms, combinatorial
geometry
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Mathematical Subject Classification 2010
Primary: 68U05
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Milestones
Received: 31 January 2014
Revised: 20 March 2014
Accepted: 1 July 2014
Published: 5 June 2015
Communicated by Kenneth S. Berenhaut
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Authors |
| Erin W. Chambers | |
| Department of Mathematics and
Computer Science Saint Louis University St. Louis, MO 63103 United States |
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| Di Fang | |
| Department of Mathematics and
Computer Science Saint Louis University St. Louis, MO 63103 United States |
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| Kyle A. Sykes | |
| Department of Mathematics and
Computer Science Saint Louis University St. Louis, MO 63103 United States |
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| Cynthia M. Traub | |
| Department of Mathematics and
Statistics Southern Illinois University Edwardsville Edwardsville, IL 62026 United States |
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| Philip Trettenero | |
| University of Illinois Urbana, IL 61801 United States |
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