When I read the HATCHER book(algebraic topolog) a question i found on a pdf and the truth is i cant find a way to solve it and realize it! the question which i saw after reading page 57/58/59( covering spaces of HATCHER) is:

> How could we find the covering space corresponding to $N=N(<a^2,b^2,(abc)^4>)$ for $S^1\vee S^1 \vee S^1$

Obviously the graph of $S^1\vee S^1 \vee S^1$ hast three orbitation and one vertex and 3 edges.

I read the HATCHER and i realize how he identified orbitations and explains covering spaces for $S^1\vee S^1$ ,but there isn't and guidness for $S^1\vee S^1 \vee S^1$ and the way to show covering spaces corresponding to i.e $N$ (converse situation explained in HATCHER)

If someone could help me to realize the way of proof and solution i would be so much grateful.

Thanks in Advance


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