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Acknowledgements To my advisor, John Shareshian. I am grateful for our many conversations and the chance to experience your viewpoint of learning and doing mathematics. Thank you for inspiring me and forming me into a better mathematician. To Jesús De Loera, from whom I learned about my thesis problem. You have been a constant source of encouragement and… (More)

Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern– Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics… (More)

- Erin W. Chambers, Di Fang, Kyle A. Sykes, Cynthia M. Traub, Philip Trettenero
- 2013

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… (More)

- Kyle A. Lawson, James L. Parish, Cynthia M. Traub, Adam G. Weyhaupt
- 2013

We obtain a complete classification of all simple closed geodesics on the eight convex deltahedra by solving a related graph coloring problem. Geodesic segments in the neighborhood of each deltahedron vertex produce a limited number of crossing angles with deltahedron edges. We define a coloring on the edge graph of a deltahedron based on these angles, and… (More)

We prove that rectangle-faced orthostacks, a restricted class of orthostacks, can be grid-edge unfolded without additional refinement. We prove several lemmas applicable to larger classes of orthostacks, and construct an example to illustrate that our algorithm does not directly extend to more general classes of orthostacks.

This paper develops techniques for computing the minimum weight Steiner triangulation of a planar point set. We call a Steiner point P a Steiner reducing point of a planar point set X if the weight (sum of edge lengths) of a minimum weight triangulation of X ∪ {P } is less than that of X. We define the Steiner reducing set St(X) to be the collection of all… (More)

- CYNTHIA M. TRAUB
- 2005

Let mwt(X) denote the sum of the Euclidean edge lengths of a minimum weight triangulation of a point set X ∈ R 2. We investigate the conditions under which an n-point set X will allow an (n + 1) st point P (called a Steiner point) to give mwt(X ∪ {P }) < mwt(X). We call the regions of the plane where such a P reduces the length of the minimum weight… (More)

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