Paper by Martin L. Demaine

Erik D. Demaine, Martin L. Demaine, and David Eppstein, “Acutely Triangulated, Stacked, and Very Ununfoldable Polyhedra”, in Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020), Saskatchewan, Saskatoon, Canada, August 5–7, 2020.

We present new examples of topologically convex edge-ununfoldable polyhedra, i.e., polyhedra that are combinatorially equivalent to convex polyhedra, yet cannot be cut along their edges and unfolded into one planar piece without overlap. One family of examples is acutely triangulated, i.e., every face is an acute triangle. Another family of examples is stacked, i.e., the result of face-to-face gluings of tetrahedra. Both families achieve another natural property, which we call very ununfoldable: for every k, there is an example such that every nonoverlapping multipiece edge unfolding has at least k pieces.

David Eppstein's presentation is available on YouTube.

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