Consider the equilateral triangle above with the vertices laid out
So I take two motions $R_1$ and $R_2$ both are reflections about their subscripted vertices and I take their composition
$R_1 R_2$ Now apparently this yields $R(120)$, a rotation of 120 cow
I don't follow this. After $R_2$ has been applied, if we reflect about vertex 1's line of symmetry (the new position), we should get $R(240)$. I computed the actual cycle permutation and it disagrees with my answer.
This is really unintuitive. I eventually figured out that the book is using the Identity's line of reflection. Why is this so confusing?