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…
Folding One Polyhedral Metric Graph into Another
Lily Chung, Erik D. Demaine, Martin L. Demaine +4
We analyze the problem of folding one polyhedron, viewed as a metric graph of its edges, into the shape of another, similar to 1D origami. We find such foldings between all pairs o…
Graph Threading with Turn Costs
Erik D. Demaine, Yael Kirkpatrick, Rebecca Lin
How should we thread a single string through a set of tubes so that pulling the string taut self-assembles the tubes into a desired graph? While prior work [ITCS 2024] solves this…
Graph Threading
Erik D. Demaine, Yael Kirkpatrick, Rebecca Lin
Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired gr…