This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333539 #30 Jul 09 2025 04:51:42 %S A333539 1,4,96,570048 %N A333539 Number of pieces formed when an n-dimensional cube is cut by all the hyperplanes defined by any n of the 2^n vertices. %D A333539 N. J. A. Sloane, Cutting Up a Cube, Math Fun Mailing List, Apr 10 2020; with replies from _Tom Karzes_, _Tomas Rokicki_, _Veit Elser_, and others. %H A333539 Veit Elser, <a href="/A333539/a333539.txt">The values of a(1) - a(4)</a> %H A333539 Scott R. Shannon, <a href="/A333539/a333539.png">Image of the 3-dimensional cube showing the 96 pieces</a>. The 4-faced polyhedra are shown in red, the 5-faced polyhedra in yellow. The later form a perfect octahedron inside the cube with its points touching the cube's inner surface. The pieces are moved away from the origin a distance proportional to the average of the distance of all its vertices from the origin. %e A333539 The two diagonals of a square cut it into four pieces, so a(2) = 4. %e A333539 For the cube the answer is 96 regions. There are 14 cuts through the cube: six cut the cube in half along a face diagonal, and eight cut off a corner with a triangle through the three adjacent corners. The cuts through the center alone divide the cube into 24 regions, and then the corner cuts further divide each of these into four regions. - _Tomas Rokicki_, Apr 11 2020 %Y A333539 For the number of hyperplanes see A007847. %Y A333539 Cf. A333540, A338571 (number of pieces for the 3D Platonic solids). %Y A333539 For a more detailed count, see A333543 and A333544. %K A333539 nonn,more %O A333539 1,2 %A A333539 _N. J. A. Sloane_, Apr 14 2020, in response to a question raised by _Scott R. Shannon_