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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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Intersections of conjugates of the icosahedral group in SO(3)

Rotate a quarter turn around the axis passing through the midpoints of two antipodal edges. That gives a different copy of the original icosahedron. A half turn preserves both icosahedra. So the state …
Wilberd van der Kallen's user avatar