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.
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
Examples
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;
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.
Crossrefs
Formula
Sum of row n = A347753(n)
Comments