4 papers
Continuous Flattening and Reversing of Convex Polyhedral Linkages
Erik D. Demaine, Martin L. Demaine, Markus Hecher +3
We prove two results about transforming any convex polyhedron, modeled as a linkage L of its edges. First, if we subdivide each edge of L in half, then L can be continuously flatte…
Complexity of Simple Folding of Mixed Orthogonal Crease Patterns
Hugo Akitaya, Josh Brunner, Erik D. Demaine +3
Continuing results from JCDCGGG 2016 and 2017, we solve several new cases of the simple foldability problem -- deciding which crease patterns can be folded flat by a sequence of (s…
Flat Folding an Unassigned Single-Vertex Complex (Combinatorially Embedded Planar Graph with Specified Edge Lengths) without Flat Angles
Lily Chung, Erik D. Demaine, Dylan Hendrickson +1
A foundational result in origami mathematics is Kawasaki and Justin's simple, efficient characterization of flat foldability for unassigned single-vertex crease patterns (where eac…
Orthogonal Fold & Cut
Hayashi Ani, Josh Brunner, Erik D. Demaine +4
We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then…