7 papers · 1 filter
Polyomino Nets Covering Three Different Boxes of Area 106 and Related Results
Erik D. Demaine, Jenny Diomidova, Nicole Jacobus +5
We present new results for polyomino nets that fold into 2 and 3 different cuboids through a computer search. The main result is the finding of 40 nets that fold into all three dif…
Undecidability of Tiling with a Tromino
ULB CompGeom Group, Zachary Abel, Hugo Akitaya +6
Given a periodic placement of copies of a tromino (either L or I), we prove co-RE-completeness (and hence undecidability) of deciding whether it can be completed to a plane tiling.…
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…
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…
Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints
NASA Space Robots Team, Josh Brunner, Kenneth C. Cheung +5
We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspec…
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…
New Results in Sona Drawing: Hardness and TSP Separation
Man-Kwun Chiu, Erik D. Demaine, Jenny Diomidova +6
Given a set of point sites, a sona drawing is a single closed curve, disjoint from the sites and intersecting itself only in simple crossings, so that each bounded region of its co…