File:Symmetries of the anharmonic group.png
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Summary
| Description |
English: The anharmonic group of permutations of the cross-ratio can be visualized as the rotation group of the trigonal dihedron, which is isomorphic to the dihedral group of the triangle D3. Considering {0, 1, ∞} as the vertices of a triangle, and the anharmonic group as its stabilizer, the fixed points of the 2-cycles are the points {−1, 1/2, 2}, which correspond to the midpoints of the edges (and the 2-cycles as rotation about that edge), and the fixed points of the 3-cycles are , which correspond to the top and bottom poles (centers of the sides; the 3-cycles correspond to rotation through their axis), and are interchanged by the 2-cycles. |
| Date | |
| Source | Own work |
| Author | Jacob Rus |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:03, 15 January 2023 | | 1,268 × 1,250 (211 KB) | wikimediacommons>Jacobolus | Uploaded own work with UploadWizard |
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