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A347918
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Irregular table read by rows: The number of k-faced polyhedra, where k >= 4, formed when a row of n adjacent cubes are internally cut by all the planes defined by any three of their vertices.
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2
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72, 24, 1472, 912, 416, 128, 32, 0, 8, 16192, 14952, 6832, 2816, 1288, 184, 80, 32, 8, 118800, 112904, 55088, 21064, 8920, 1560, 736, 232, 112
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history;
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OFFSET
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1,1
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COMMENTS
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See A347753 for an explanation of the sequence and additional images.
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LINKS
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Scott R. Shannon, Image showing the 319416 different k-faced polyhedra for 4 adjacent cubes. The 4-, 5-, 6-, 7-, 8-, and 9-faced polyhedra are colored red, orange, yellow, green, blue, indigo respectively. The 10-, 11-, and 12-faced polyhedra, which are not visible on the surface and are shown together, are colored violet, white, black.
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FORMULA
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EXAMPLE
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The single cube, row 1, is internally cut with 14 planes which creates seventy-two 4-faced polyhedra and twenty-four 5-faced polyhedra. See also A333539.
The table begins:
72, 24;
1472, 912, 416, 128, 32, 0, 8;
16192, 14952, 6832, 2816, 1288, 184, 80, 32, 8;
118800, 112904, 55088, 21064, 8920, 1560, 736, 232, 112;
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CROSSREFS
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KEYWORD
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nonn,more,tabf
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AUTHOR
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STATUS
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approved
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