Folding Polyiamonds into Octahedra

  title={Folding Polyiamonds into Octahedra},
  author={Eva Bolle and Linda Kleist},
  journal={Comput. Geom.},



Folding Polyominoes into (Poly)Cubes

A linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models is given and the triangular version of the problem is considered, characterizing which polyiamonds fold into a regular tetrahedron.

Folding Small Polyominoes into a Unit Cube

It is demonstrated that a 3×3 square can fold into a unit cube using horizontal, vertical, and diagonal creases on the 6× 6 half-grid, implying that all tree-shaped polyominoes with at least nine squares fold intoA unit cube.

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Common Unfoldings of Polyominoes and Polycubes

It is shown here that all 23 tree-like pentacubes have no such common unfolding, although 22 of them have a common unfolding.

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This paper first shows that there is an orthogonal polygon that fold to three boxes of size 1×1×5, 1 × 2 × 3, and 0 × 1 × 11, which solves the open problem mentioned in literature and shows some polygons that can fold to two incongruent Orthogonal boxes in more general directions.

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It is an open question which polycubes are rigidly foldable from a particular cube gadget, though it seems through simple empirical testing that the authors' cube gadgets fold rigidly in isolation (when making one-cubepolycubes).

Common developments of three incongruent boxes of area 30

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