Three-dimensional edge-matching puzzle

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A three-dimensional edge-matching puzzle is a type of edge-matching puzzle or tiling puzzle involving tiling a three-dimensional area with (typically regular) polygonal pieces whose edges are distinguished with colors or patterns, in such a way that the edges of adjacent pieces match. Edge-matching puzzles are known to be NP-complete, and capable of conversion to and from equivalent jigsaw puzzles and polyomino packing puzzle. [1]

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Three-dimensional edge-matching puzzles are not currently under direct U.S. patent protection, since the 1892 patent by E. L. Thurston has expired. [2]

Current examples of commercial three-dimensional edge-matching puzzles include the Dodek Duo, The Enigma, Mental Misery, [3] and Kadon Enterprises' range of three-dimensional edge-matching puzzles. [4]

See also

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An edge-matching puzzle is a type of tiling puzzle involving tiling an area with polygons whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match.

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A hinged dissection, also known as a swing-hinged dissection or Dudeney dissection, is a kind of geometric dissection in which all of the pieces are connected into a chain by "hinged" points, such that the rearrangement from one figure to another can be carried out by swinging the chain continuously, without severing any of the connections. Typically, it is assumed that the pieces are allowed to overlap in the folding and unfolding process; this is sometimes called the "wobbly-hinged" model of hinged dissection.

Conway criterion

In the mathematical theory of tessellations, the Conway criterion, named for the English mathematician John Horton Conway, describes rules for when a prototile will tile the plane; it consists of the following requirements: The tile must be a closed topological disk with six consecutive points A, B, C, D, E, and F on the boundary such that:

Serpentiles is the name coined by Kurt N. Van Ness for the hexagonal tiles used in various edge-matching puzzle abstract strategy games, such as Psyche-Paths, Kaliko, and Tantrix. For each tile, one to three colors are used to draw paths linking the six sides together in various configurations. Each side is connected to another side by a specific path route and color. Gameplay generally proceeds so that players take turns laying down tiles. During each turn, a tile is laid adjacent to existing tiles so that colored paths are contiguous across tile edges.

References

  1. Erik D. Demaine, Martin L. Demaine. "Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity" (PDF). Retrieved 2007-08-12.
  2. "Rob's puzzle page: Edge Matching" . Retrieved 2007-08-12.
  3. "Rob's puzzle page: Pattern Puzzles" . Retrieved 2009-06-22.
  4. "Kadon Enterprises, More About Edgematching" . Retrieved 2009-06-22.