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All Polyhedral Manifolds are Connected by a 2-Step Refolding
Lily Chung, Erik D. Demaine, Jenny Diomidova +4
We prove that, for any two polyhedral manifolds , there is a polyhedral manifold such that share a common unfolding an…
Dudeney's Dissection is Optimal
Erik D. Demaine, Tonan Kamata, Ryuhei Uehara
In 1907, Henry Ernest Dudeney posed a puzzle: ``cut any equilateral triangle \dots\ into as few pieces as possible that will fit together and form a perfect square'' (without overl…
All Polyhedral Manifolds are Connected by a 2-Step Refolding
Lily Chung, Erik D. Demaine, Jenny Diomidova +4
We prove that, for any two polyhedral manifolds , there is a polyhedral manifold such that share a common unfolding and…
Any Regular Polyhedron Can Transform to Another by O(1) Refoldings
Erik D. Demaine, Martin L. Demaine, Jenny Diomidova +3
We show that several classes of polyhedra are joined by a sequence of O(1) refolding steps, where each refolding step unfolds the current polyhedron (allowing cuts anywhere on the…
Efficient Folding Algorithms for Regular Polyhedra
Tonan Kamata, Akira Kadoguchi, Takashi Horiyama +1
We investigate the folding problem that asks if a polygon P can be folded to a polyhedron Q for given P and Q. Recently, an efficient algorithm for this problem has been developed…