485 citations · 940 across the 12 of their papers we have counts for
6 papers · 1 filter
Geodesic Folding of Tetrahedron
Seri Nishimoto, Takashi Horiyama, Tomohiro Tachi
In this work, we show the geometric properties of a family of polyhedra obtained by folding a regular tetrahedron along regular triangular grids. Each polyhedron is identified by a…
Conic Crease Patterns with Reflecting Rule Lines
Erik D. Demaine, Martin L. Demaine, David A. Huffman +2
We characterize when two conic curved creases are compatible with each other, when the rule lines must converge to conic foci and reflect at the crease. Namely, two conics are comp…
Rigid Foldability is NP-Hard
Hugo Akitaya, Erik D. Demaine, Takashi Horiyama +3
In this paper, we show that deciding rigid foldability of a given crease pattern using all creases is weakly NP-hard by a reduction from Partition, and that deciding rigid foldabil…
An Edge Extrusion-Approach to Generate Extruded Miura-Ori and Its Double Tiling Origami Patterns
Kai Suto, Akito Adachi, Tomohiro Tachi +1
This paper proposes a family of origami tessellations called extruded Miura-Ori, whose folded state lies between two parallel planes with some faces on the planes, potentially usef…
Characterization of Curved Creases and Rulings: Design and Analysis of Lens Tessellations
Erik D. Demaine, Martin L. Demaine, David A. Huffman +2
We describe a general family of curved-crease folding tessellations consisting of a repeating "lens" motif formed by two convex curved arcs. The third author invented the first suc…
(Non)existence of Pleated Folds: How Paper Folds Between Creases
Erik D. Demaine, Martin L. Demaine, Vi Hart +2
We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical m…