Symmetries_of_the_anharmonic_group.png
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Summary
Description Symmetries of the anharmonic group.png |
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
D
3
.
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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