Free Product of $\mathbb Z_3$ and $\mathbb Z_4$

I was recently tasked to draw the Cayley diagram of the free product of $\Z_3$ and $\Z_4$. It looks quite nice and interesting (to me anyway), so why not put it up here?

I don’t understand free products well enough to be able to explain them in any manner, but that doesn’t prevent me from sharing the diagram with you! Here you go:

A small portion of $\Z_3\star\Z_4$