File:Inverses in the hexadecachoric group, PT.png
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Summary
[edit]| Description |
   Permutations in the hyperoctahedral group of order 4 (arranged as in the lattice) Coarsely, this image simply shows the permutohedron with edges between inverse vertices (of types white, orange). The following dictionary shows this assignment, including the tesseract permutations in cycle notation: edge_bundles = {
# neutral (self-inverse)
0: {'pair': (0, 0), 'cycles': []},
# bold (self-inverse)
7: {'pair': (0, 7), 'cycles': [[1, 2], [4, 8], [5, 10], [6, 9], [7, 11], [13, 14]]},
16: {'pair': (0, 16), 'cycles': [[1, 4], [2, 8], [3, 12], [6, 9], [7, 13], [11, 14]]},
23: {'pair': (0, 23), 'cycles': [[1, 8], [2, 4], [3, 12], [5, 10], [7, 14], [11, 13]]},
# white
3: {'pair': (0, 4), 'cycles': [[1, 2, 4], [3, 6, 5], [9, 10, 12], [11, 14, 13]]},
4: {'pair': (0, 3), 'cycles': [[1, 4, 2], [3, 5, 6], [9, 12, 10], [11, 13, 14]]},
8: {'pair': (0, 12), 'cycles': [[2, 4, 8], [3, 5, 9], [6, 12, 10], [7, 13, 11]]},
12: {'pair': (0, 8), 'cycles': [[2, 8, 4], [3, 9, 5], [6, 10, 12], [7, 11, 13]]},
11: {'pair': (0, 19), 'cycles': [[1, 4, 8], [3, 6, 10], [5, 12, 9], [7, 14, 11]]},
19: {'pair': (0, 11), 'cycles': [[1, 8, 4], [3, 10, 6], [5, 9, 12], [7, 11, 14]]},
15: {'pair': (0, 20), 'cycles': [[1, 2, 8], [3, 10, 9], [5, 6, 12], [7, 14, 13]]},
20: {'pair': (0, 15), 'cycles': [[1, 8, 2], [3, 9, 10], [5, 12, 6], [7, 13, 14]]},
# green (self-inverse)
1: {'pair': (0, 1), 'cycles': [[1, 2], [5, 6], [9, 10], [13, 14]]},
2: {'pair': (0, 2), 'cycles': [[2, 4], [3, 5], [10, 12], [11, 13]]},
6: {'pair': (0, 6), 'cycles': [[4, 8], [5, 9], [6, 10], [7, 11]]},
5: {'pair': (0, 5), 'cycles': [[1, 4], [3, 6], [9, 12], [11, 14]]},
14: {'pair': (0, 14), 'cycles': [[2, 8], [3, 9], [6, 12], [7, 13]]},
21: {'pair': (0, 21), 'cycles': [[1, 8], [3, 10], [5, 12], [7, 14]]},
# orange
9: {'pair': (0, 18), 'cycles': [[1, 2, 4, 8], [3, 6, 12, 9], [5, 10], [7, 14, 13, 11]]},
18: {'pair': (0, 9), 'cycles': [[1, 8, 4, 2], [3, 9, 12, 6], [5, 10], [7, 11, 13, 14]]},
10: {'pair': (0, 13), 'cycles': [[1, 4, 8, 2], [3, 5, 12, 10], [6, 9], [7, 13, 14, 11]]},
13: {'pair': (0, 10), 'cycles': [[1, 2, 8, 4], [3, 10, 12, 5], [6, 9], [7, 11, 14, 13]]},
17: {'pair': (0, 22), 'cycles': [[1, 4, 2, 8], [3, 12], [5, 6, 10, 9], [7, 14, 11, 13]]},
22: {'pair': (0, 17), 'cycles': [[1, 8, 2, 4], [3, 12], [5, 9, 10, 6], [7, 13, 11, 14]]},
}
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| current | 00:25, 8 March 2020 | | 3,800 × 4,000 (3.74 MB) | Watchduck (talk | contribs) |
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