File:Symmetric group 4; permutohedron 3D; numbers.svg
Summary
| Description |
 Permutohedron of the symmetric group S4 The vertices are labelled with the index numbers of the permutations shown in the file on the right.  |
||
| Date | |||
| Source | Own work | ||
| Author |
|
||
| Other versions |
 |
||
| SVG development |
The following dictionary shows the vertices' coordinates in this right-handed coordinate system:
.png){kind=link}
coordinates = {
0: ( 0,-1,-2),
1: (-1, 0,-2),
2: ( 0,-2,-1),
3: (-2, 0,-1),
4: (-1,-2, 0),
5: (-2,-1, 0),
6: ( 1, 0,-2),
7: ( 0, 1,-2),
8: ( 1,-2, 0),
9: (-2, 1, 0),
10: ( 0,-2, 1),
11: (-2, 0, 1),
12: ( 2, 0,-1),
13: ( 0, 2,-1),
14: ( 2,-1, 0),
15: (-1, 2, 0),
16: ( 0,-1, 2),
17: (-1, 0, 2),
18: ( 2, 1, 0),
19: ( 1, 2, 0),
20: ( 2, 0, 1),
21: ( 0, 2, 1),
22: ( 1, 0, 2),
23: ( 0, 1, 2),
}
These are the 36 upward edges:
edges = [(0, 1), (0, 2), (0, 6), (1, 3), (1, 7), (2, 4), (2, 8), (3, 5), (3, 9), (4, 5), (4, 10), (5, 11), (6, 7), (6, 12), (7, 13), (8, 10), (8, 14), (9, 11), (9, 15), (10, 16), (11, 17), (12, 14), (12, 18), (13, 15), (13, 19), (14, 20), (15, 21), (16, 17), (16, 22), (17, 23), (18, 19), (18, 20), (19, 21), (20, 22), (21, 23), (22, 23)]
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
 |
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.