This paper "Local connectivity of Julia sets and bifuraction loci:three theorems of J.C.Yoccoz"(see http://pi.math.cornell.edu/~hubbard/Yoccoz.pdf) tells that it is quite easy to construct the topology of a puzzle to a given deoth by hand(see Remark 5.3). I wonder that for the 1/3-limb, we know that there are three external rays landing at the repelling fixed points $\alpha$, then it is easy to know the knowledge at depth-0, then the topology of depth-1 can be got by mapping each puzzle at depth-0 under $f^{-1}$, now I am a little confuse that how do we know the position of the perimage of $\alpha$, i.e. how do we know which piece does $f^{-1}(\alpha)$ belong to? Furthermore, how do we know that the topology of a puzzle at depth-2, or depth-n? Are there any more details can I get from here?