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

1,1

Comments

See A347753 for an explanation of the sequence and additional images.

See A333539 and A338622 for images of the single cube.

Links

Table of n, a(n) for n=1..27.

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

Adjacent sequences: A347915 A347916 A347917 * A347919 A347920 A347921

Keyword

nonn,more,tabf

Author

Scott R. Shannon, Sep 19 2021

Status

approved