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A333539
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Number of pieces formed when an n-dimensional cube is cut by all the hyperplanes defined by any n of the 2^n vertices.
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12
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OFFSET
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1,2
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REFERENCES
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LINKS
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Scott R. Shannon, Image of the 3-dimensional cube showing the 96 pieces. The 4-faced polyhedra are shown in red, the 5-faced polyhedra in yellow. The later form a perfect octahedron inside the cube with its points touching the cube's inner surface. The pieces are moved away from the origin a distance proportional to the average of the distance of all its vertices from the origin.
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EXAMPLE
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The two diagonals of a square cut it into four pieces, so a(2) = 4.
For the cube the answer is 96 regions. There are 14 cuts through the cube: six cut the cube in half along a face diagonal, and eight cut off a corner with a triangle through the three adjacent corners. The cuts through the center alone divide the cube into 24 regions, and then the corner cuts further divide each of these into four regions. - Tomas Rokicki, Apr 11 2020
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CROSSREFS
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For the number of hyperplanes see A007847.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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