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Reference.org
Three-dimensional edge-matching puzzle
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<p>A three-dimensional edge-matching puzzle is a type of <a href="/facts/Edge-matching_puzzle/RYY7DHhJ">edge-matching puzzle</a> or <a href="/facts/Tiling_puzzle/c9JPlarv">tiling puzzle</a> involving <a href="/facts/Tiling_(mathematics)/7BWDywXC">tiling</a> a three-dimensional area with (typically regular) <a href="/facts/Polygon/xvkmYhvG">polygonal</a> 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 <a href="/facts/NP-complete/NFPv56DU">NP-complete</a>, and capable of conversion to and from equivalent <a href="/facts/Jigsaw_puzzle/pPDDQGqE">jigsaw puzzles</a> and <a href="/facts/Polyomino/XUlHFIRY">polyomino</a> packing puzzle. </p><p>Three-dimensional edge-matching puzzles are not currently under direct U.S. patent protection, since the 1892 patent by E. L. Thurston has expired. </p><p>Current examples of commercial three-dimensional edge-matching puzzles include the Dodek Duo, The Enigma, Mental Misery, and Kadon Enterprises' range of three-dimensional edge-matching puzzles. </p>