Hinged Dissections Exist
نویسندگان
چکیده
منابع مشابه
Hinged dissections of polyominoes and polyforms
This paper shows how to hinge together a collection of polygons at vertices in such a way that a single object can be reshaped into any n-omino, for a given value of n. An n-omino is de ned generally as a connected union of n unit squares on the integer grid. Our best dissection uses 2(n 1) polygons. We generalize this result to the connected unions of nonoverlapping equal-size regular k-gons j...
متن کاملThe Manifold Beauty of Piano-hinged Dissections
A geometric dissection is a cutting of one geometric figure into pieces that we can rearrange to form another. For some dissections, it is possible to hinge the pieces together, so that we can flip the pieces one way on the hinges to form one figure, and flip them another way to form the other figure. When the hinge connects two pieces along a shared edge in both target figures, the movement co...
متن کاملComputational Complexity of Piano-Hinged Dissections
We prove NP-completeness of deciding whether a given loop of colored right isosceles triangles, hinged together at edges, can be folded into a specified rectangular three-color pattern. By contrast, the same problem becomes polynomially solvable with one color or when the target shape is a tree-shaped polyomino.
متن کاملPolyhedral Characterization of Reversible Hinged Dissections
We prove that two polygons A and B have a reversible hinged dissection (a chain hinged dissection that reverses inside and outside boundaries when folding between A and B) if and only if A and B are two non-crossing nets of a common polyhedron. Furthermore, monotone hinged dissections (where all hinges rotate in the same direction when changing from A to B) correspond exactly to non-crossing ne...
متن کاملSymmetry and Structure in Twist-Hinged Dissections of Polygonal Rings and Polygonal Anti-Rings
A geometric dissection is a cutting of a geometric figure into pieces that we can rearrange to form another figure. Twist-hinged dissections have the amazing property that all pieces are connected by special hinges that allow the one figure to be converted to the other by means of twists. This paper explores such dissections for ringlike figures based on regular polygons. The twist-hinged disse...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2011
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-010-9305-9