File:Symmetric group 4; permutohedron 3D; numbers.svg
Summary
| Description |
English:
Permutohedron of the symmetric group S4
The vertices are labelled with the index numbers of the permutations shown in the file on the left. |
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| Source | Own work | ||
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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)]
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