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polycube
A polycube is a solid figure formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes.〔(Weisstein, Eric W. "Polycube." From MathWorld )〕
==Enumerating polycubes==
Like polyominoes, polycubes can be enumerated in two ways, depending on whether chiral pairs of polycubes are counted as one polycube or two.〔("Enumeration of Specific Classes of Polycubes", Jean-Marc Champarnaud et al, Université de Rouen, France ) PDF〕 For example, 6 tetracubes have mirror symmetry and one is chiral, giving a count of 7 or 8 tetracubes respectively. Unlike polyominoes, polycubes are usually counted with mirror pairs distinguished, because one cannot turn a polycube over to reflect it as one can a polyomino. In particular, the Soma cube uses both forms of the chiral tetracube.
Polycubes are classified according to how many cubical cells they have:〔(Polycubes, at The Poly Pages )〕
Polycubes have been enumerated up to ''n''=16.〔("Dirichlet convolution and enumeration of pyramid polycubes", C. Carré, N. Debroux, M. Deneufchâtel, J. Dubernard, C. Hillairet, J. Luque, O. Mallet; November 19, 2013 ) PDF〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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