  We establish basic geometric and topological properties of Thurston's Master
Teapot and the Thurston set for superattracting unimodal self-maps of
intervals. In particular, the Master Teapot is connected, contains the unit
cylinder, and its intersection with a set $\mathbb{D} \times \{c\}$ grows
monotonically with $c$. We show that the Thurston set described above is not
equal to the Thurston set for postcritically finite tent maps, and we provide
an arithmetic explanation for why certain gaps appear in plots of finite
approximations of the Thurston set.
