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

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Original file ‎(SVG file, nominally 744 × 744 pixels, file size: 74 KB)

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Summary[edit]

Description
Permutohedron with permutations as coordinates

Permutohedron of the symmetric group S4

The vertices are labelled with the index numbers of the permutations shown in the file on the right.
E.g. (3, 1, 2, 4) has the index number 3. Compare this list.

Corresponding Schlegel diagram
Date
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Other versions
Labelled with inverse permutations (like the Cayley graph)
SVG development
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This SVG file was uploaded with Commonist.

The following dictionary shows the vertices' coordinates in this right-handed coordinate system: 

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[edit]

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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attribution
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.

File history

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Date/TimeThumbnailDimensionsUserComment
current09:19, 20 March 2022Thumbnail for version as of 09:19, 20 March 2022744 × 744 (74 KB)Watchduck (talk | contribs)Revert. Image size and transparency were messed up.
14:11, 19 March 2022Thumbnail for version as of 14:11, 19 March 2022512 × 411 (17 KB)TSamuel (talk | contribs)Lossless recompression via SVGOMG, vecta.io/nano, & Compress-Or-Die.com, & verified via SVGCheck
22:23, 13 August 2010Thumbnail for version as of 22:23, 13 August 2010744 × 744 (74 KB)Watchduck (talk | contribs)made 18 translucent
00:05, 9 August 2010Thumbnail for version as of 00:05, 9 August 2010744 × 744 (75 KB)Watchduck (talk | contribs)

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