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Given a polygon P in the plane, a pop operation is the reflection of a vertex with respect to the line through its adjacent vertices. We define a family of alternating polygons, and show that any polygon from this family cannot be convexified by pop operations. This family contains simple, as well as non-simple (i.e., self-intersecting) polygons, as… (More)

A configuration of unit cubes in three dimensions with integer coordinates is called an animal if the boundary of their union is home-omorphic to a sphere. Shermer discovered several animals from which no single cube may be removed such that the resulting configurations are also animals [16]. Here we obtain a dual result: we give an example of an animal to… (More)

A length preserving transformation of a polygon is any transformation of its vertices that preserves the lengths of the edges. In the video segment we will demonstrate three types of length preserving transformations: pocket flips, flipturns, and pops. We present sequences of such operations and study their power (or weakness) in the attempt of convexifying… (More)

- Milos Stojakovic, David M. Mount, Sergio Cabello, Bojan Moliar, Pankaj K. Agarwal, Rinat Ben Avraham +14 others
- 2010

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