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Suppose we take the circle $S_1$ and three points on this circle, which defines a triangle. By moving the points continuously on $S_1$, we obtain a continuous transformation of the triangle.

I was wondering what is the structure of this group of transformations ?

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    it seems like $S^1\times S^1\times S^1$ as you can move each vertex individually, unless you start identifying various configurations like $(\theta,\theta,\theta)=(0,0,0)$2011-03-21
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    @yoyo: I think that only holds if you label each vertex and allow "triangles" which have two or three overlapping points.2011-03-21

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