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  1. No Access

    Chapter and Conference Paper

    Universal Hinge Patterns for Folding Strips Efficiently into Any Grid Polyhedron

    We present two universal hinge patterns that enable a strip of material to fold into any connected surface made up of unit squares on the 3D cube grid—for example, the surface of any polycube. The folding is e...

    Nadia M. Benbernou, Erik D. Demaine, Martin L. Demaine… in Algorithms and Data Structures (2017)

  2. No Access

    Chapter

    Variations on Instant Insanity

    In one of the first papers about the complexity of puzzles, Robertson and Munro [14] proved that a generalized form of the then-popular Instant Insanity puzzle is NP-complete. Here we study several variations ...

    Erik D. Demaine, Martin L. Demaine… in Space-Efficient Data Structures, Streams, … (2013)

  3. No Access

    Chapter and Conference Paper

    Folding Equilateral Plane Graphs

    We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical con...

    Zachary Abel, Erik D. Demaine, Martin L. Demaine… in Algorithms and Computation (2011)

  4. No Access

    Chapter and Conference Paper

    Algorithms for Solving Rubik’s Cubes

    The Rubik’s Cube is perhaps the world’s most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik’s Cube also has a rich u...

    Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw… in Algorithms – ESA 2011 (2011)

  5. No Access

    Chapter and Conference Paper

    Minimal Locked Trees

    Locked tree linkages have been known to exist in the plane since 1998, but it is still open whether they have a polynomial-time characterization. This paper examines the properties needed for planar trees to l...

    Brad Ballinger, David Charlton, Erik D. Demaine… in Algorithms and Data Structures (2009)

  6. No Access

    Chapter and Conference Paper

    Hinged Dissection of Polypolyhedra

    This paper presents a general family of 3D hinged dissections for polypolyhedra, i.e., connected 3D solids formed by joining several rigid copies of the same polyhedron along identical faces. (Such joinings are p...

    Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lindy… in Algorithms and Data Structures (2005)

  7. No Access

    Chapter and Conference Paper

    When Can You Fold a Map?

    We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are se...

    Esther M. Arkin, Michael A. Bender, Erik D. Demaine… in Algorithms and Data Structures (2001)