8 citations · 12 across the 4 of their papers we have counts for
14 papers · 1 filter
A Universal Crease Pattern for Folding Orthogonal Shapes
Nadia Benbernou, Erik D. Demaine, Martin L. Demaine +1
We present a universal crease pattern--known in geometry as the tetrakis tiling and in origami as box pleating--that can fold into any object made up of unit cubes joined face-to-f…
Cauchy's Arm Lemma on a Growing Sphere
Zachary Abel, David Charlton, Sebastien Collette +6
We propose a variant of Cauchy's Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its en…
Staged Self-Assembly:Nanomanufacture of Arbitrary Shapes with O(1) Glues
Erik D. Demaine, Martin L. Demaine, Sandor P. Fekete +4
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model an…
A Locked Orthogonal Tree
David Charlton, Erik D. Demaine, Martin L. Demaine +2
We give a counterexample to a conjecture of Poon [Poo06] that any orthogonal tree in two dimensions can always be flattened by a continuous motion that preserves edge lengths and a…
Hinged Dissections Exist
Timothy G. Abbott, Zachary Abel, David Charlton +3
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged a…
Enumerating Foldings and Unfoldings between Polygons and Polytopes
Erik D. Demaine, Martin L. Demaine, Anna Lubiw +1
We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous quest…