cp's OEIS Frontend

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.

%I A347918 #15 Sep 20 2021 22:12:10
%S A347918 72,24,1472,912,416,128,32,0,8,16192,14952,6832,2816,1288,184,80,32,8,
%T A347918 118800,112904,55088,21064,8920,1560,736,232,112
%N 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.
%C A347918 See A347753 for an explanation of the sequence and additional images.
%C A347918 See A333539 and A338622 for images of the single cube.
%H A347918 Scott R. Shannon, <a href="/A347918/a347918.png">Image showing the 319416 different k-faced polyhedra for 4 adjacent cubes</a>. 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.
%F A347918 Sum of row n = A347753(n)
%e A347918 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.
%e A347918 The table begins:
%e A347918       72,     24;
%e A347918     1472,    912,   416,   128,   32,    0,   8;
%e A347918    16192,  14952,  6832,  2816, 1288,  184,  80,  32,   8;
%e A347918   118800, 112904, 55088, 21064, 8920, 1560, 736, 232, 112;
%Y A347918 Cf. A347753 (total number of polyhedra), A333539 (n-dimensional cube), A338622 (Platonic solids), A338801 (n-prism), A338825 (n-bipyramid).
%K A347918 nonn,more,tabf
%O A347918 1,1
%A A347918 _Scott R. Shannon_, Sep 19 2021