|
|
A338622
|
|
Irregular table read by rows: The number of k-faced polyhedra, where k>=4, formed when the five Platonic solids, in the order tetrahedron, octahedron, cube, icosahedron, dodecahedron, are internally cut by all the planes defined by any three of their vertices.
|
|
13
|
|
|
1, 8, 72, 24, 2160, 360, 205320, 208680, 94800, 34200, 7920, 1560, 120
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
See A338571 for further details and images of this sequence.
The author thanks Zach J. Shannon for producing the images for this sequence.
|
|
LINKS
|
Scott R. Shannon, Octahedron, showing the 8 4-faced polyhedra post-cutting. The octahedron has 3 internal cutting planes, each along the 2D axial planes. For clarity in this image, and the two cube images, the pieces are moved away from the origin a distance proportional to the average distance of their vertices from the origin.
|
|
FORMULA
|
|
|
EXAMPLE
|
The cube is cut with 14 internal planes defined by all 3-vertex combinations of its 8 vertices. This leads to the creation of 72 4-faced polyhedra and 24 5-faced polyhedra, 96 pieces in all. See A338571 and A333539.
The table is:
1;
8;
72, 24;
2160, 360;
205320, 208680, 94800, 34200, 7920, 1560, 120;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,fini,full,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|