  We prove that the bicanonical map of the Cartwright-Steger surface is an
embedding. We also discuss two minimal surfaces of general type, both covered
by the Cartwright-Steger surface. One has $K^2=2$, $p_g=1$, $\pi_1=\{1\}$ and
the other has $K^2=1$, $p_g=0$, $\pi_1=\mathbb{Z}/2\mathbb{Z}$.
