File:Symmetric group 4; permutohedron 3D; transpositions (1-based).png

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the six edge directions

Permutohedron of the symmetric group S4

Parallel edges have the same color. The color shows which two places are swapped, as indicated by the triangle of pairs in the bottom right corner.
In the bottom vertex of an edge the elements on these two places are in their natural order, and in the top vertex they are reversed.
(Consequently, the bottom vertex of the whole diagram is completely in natural order, and the top vertex is completely reversed.)

 
This image was created with POV-Ray.
trunc_octa_perm.pov
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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current18:06, 17 January 2020Thumbnail for version as of 18:06, 17 January 20203,900 × 4,000 (1.36 MB)Watchduck (talk | contribs)User created page with UploadWizard

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