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A347918
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.
2
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
OFFSET
1,1
COMMENTS
See A347753 for an explanation of the sequence and additional images.
See A333539 and A338622 for images of the single cube.
LINKS
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.
FORMULA
Sum of row n = A347753(n)
EXAMPLE
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;
CROSSREFS
Cf. A347753 (total number of polyhedra), A333539 (n-dimensional cube), A338622 (Platonic solids), A338801 (n-prism), A338825 (n-bipyramid).
Sequence in context: A249700 A036178 A036187 * A035879 A033392 A304262
KEYWORD
nonn,more,tabf
AUTHOR
Scott R. Shannon, Sep 19 2021
STATUS
approved