File:Full octahedral group; inversion lattice; inversion sets.svg

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Original file ‎(SVG file, nominally 980 × 980 pixels, file size: 3.44 MB)

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Summary

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Description

Lattice of inversion sets of the octahedral group

This graph has 48 vertices and 64 edges.
The 32 vertices with brown background have degree 3. The 16 with green background have degree 2.
The light and dark shades change with every arrow.

Red hexagons indicate, that an inversion is part of the set.
To the left of each triangle is the pair of row and column, denoting the signed permutation.
To its right is the inversion number, i.e. the number red hexagons.

S4 based labels
8×6 matrix
8 choose 2 array
This SVG was created with Inkscape.
This file contains an Inkscape grid, which makes it an invalid SVG.
This does no harm at all, and there is no reason to remove it.

The code of this file is much bigger than it should be. The content of the 8×6 file was copied into Inkscape, and that has replaced the clones by objects.

Date
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Other versions
This is the equivalent for the symmetry group of the square.
It corresponds to the outer octagon.

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 4.0 International 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.

File history

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Date/TimeThumbnailDimensionsUserComment
current22:54, 10 March 2024Thumbnail for version as of 22:54, 10 March 2024980 × 980 (3.44 MB)Watchduck (talk | contribs)subdivide triangles
21:42, 7 March 2024Thumbnail for version as of 21:42, 7 March 2024980 × 980 (3.39 MB)Watchduck (talk | contribs)vertical flip
19:23, 6 March 2024Thumbnail for version as of 19:23, 6 March 2024980 × 980 (3.39 MB)Watchduck (talk | contribs)Uploaded own work with UploadWizard

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