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File:Symmetric group 4; permutohedron 3D; transpositions.svg

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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.)
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Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Other versions
Raytraced version
Versions with left/right inversion counts below the permutations
In these files the six edge colors are reduced to three: The decreasing/increasing diagonals of the triangle are bundled to blue, green and red.

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I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head 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.
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Date/TimeThumbnailDimensionsUserComment
current17:58, 17 January 2020Thumbnail for version as of 17:58, 17 January 2020693 × 711 (131 KB)Watchduck (talk | contribs)slightly darker colors
14:25, 6 January 2020Thumbnail for version as of 14:25, 6 January 2020693 × 711 (132 KB)Watchduck (talk | contribs)User created page with UploadWizard

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