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Polycube
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==Properties of pentacubes== 12 pentacubes are flat and correspond to the [[pentomino]]es. 5 of the remaining 17 have mirror symmetry, and the other 12 form 6 chiral pairs. The bounding boxes of the pentacubes have sizes 5Γ1Γ1, 4Γ2Γ1, 3Γ3Γ1, 3Γ2Γ1, 3Γ2Γ2, and 2Γ2Γ2.<ref>[[Ronald Aarts|Aarts, Ronald M.]] [http://mathworld.wolfram.com/Pentacube.html "Pentacube"]. From MathWorld.</ref> A polycube may have up to 24 orientations in the cubic lattice, or 48, if reflection is allowed. Of the pentacubes, 2 flats (5-1-1 and the cross) have mirror symmetry in all three axes; these have only three orientations. 10 have one mirror symmetry; these have 12 orientations. Each of the remaining 17 pentacubes has 24 orientations.
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