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An edge-matching puzzle is a type of tiling puzzle involving tiling an area with (typically regular) polygons whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match. Edge-matching puzzles are known to be NP-complete, and adaptable for conversion to and from equivalent jigsaw puzzles and ...
Each of the six faces is a different colour, but each of the nine pieces on a face is identical in colour in the solved condition. In the unsolved condition, colours are distributed amongst the pieces of the cube. Puzzles like the Rubik's Cube which are manipulated by rotating a section of pieces are popularly called twisty puzzles. They are ...
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 ...
The MacMahon Squares game is an example of an edge-matching puzzle. The family of such problems is NP-complete . The first part of New Mathematical Diversions describes these games in general, starting with linear forms ( dominoes ), then progressing in detail with similar games using tiles shaped as equilateral triangles, squares, right ...
Unlike the original puzzle (but like the 4×4×4 cube), it has no fixed facets: the center facets (16 per face) are free to move to different positions. Methods for solving the 3×3×3 cube work for the edges and corners of the 6×6×6 cube, as long as one has correctly identified the relative positions of the colors — since the center facets ...
The cube stacking game is a two-player game version of this puzzle. Given an ordered list of cubes, the players take turns adding the next cube to the top of a growing stack of cubes. Given an ordered list of cubes, the players take turns adding the next cube to the top of a growing stack of cubes.
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The relations can be made apparent by examining the vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive). For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces. The possible faces are 3 - equilateral ...
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