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Every quadratic rational map with a period $3$ critical point is 
represented up to M\"obius conjugacy by
$$h_{a}(z)={(z-a)(z-1)\over z^{2}}.$$
The critical points are $0$ and $c_{2}(a)=\displaystyle{{2a\over a+1}}$ and $0$ 
is of period $3$. In fact:
$$h_{a}(0)=\infty ,\ \ h_{a}(\infty )=1,\ \ h_{a}(1)=0,$$
$$h_{a}(c_{2}(a)) =-{(a-1)^{2}\over 4a}=v_{2}(a),\ \ 
h_{a}^{-1}(0)=\{ 1,a\} ,\ \ h_{a}^{-1}(1)=\left \{ \infty ,{a\over 
a+1}\right \} .$$
Write
$$V_{3}=\{ h_{a}:a\in \mathbb C,\ a\neq 0\} .$$


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