Paper by Erik D. Demaine

Elena Arseneva, Erik D. Demaine, Tonan Kamata, and Ryuhei Uehara, “Discretization to Prove the Nonexistence of “Small” Common Unfoldings Between Polyhedra”, in Proceedings of the 34th Canadian Conference on Computational Geometry (CCCG 2022), Toronto, Ontario, Canada, August 25–27, 2022, to appear.

We show that no < 300-gon is a common unfolding between any two doubly covered triangles whose angles are rationally independent algebraic numbers. Here an unfolding of a polyhedron is a polygon obtained by cutting anywhere on the polyhedron's surface and unfolding it.

The paper is 7 pages.

The paper is available in PDF (1407k).
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Last updated August 19, 2022 by Erik Demaine.