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cs.CG2026
Overlapping Unfoldings of Cones and Convex Polyhedra
MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine +4
Research on Dürer's problem focuses on edge unfoldings of convex polyhedra that avoid overlap. We invert the goal and find unfoldings that overlap at some point to any given thick…
cs.CG2025
Undecidability of Tiling with a Tromino
ULB CompGeom Group, Zachary Abel, Hugo Akitaya +6
Given a periodic placement of copies of a tromino (either L or I), we prove co-RE-completeness (and hence undecidability) of deciding whether it can be completed to a plane tiling.…
cs.CG2024
Tiling with Three Polygons is Undecidable
Erik D. Demaine, Stefan Langerman
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of th…