  We classify the periodic digit strings which arise from periodic billiard
orbits on the four convex $n$-gons $\Delta$ which tile $\mathbb{R}^2$ under
reflection, answering problem a posed by Baxter and Umble. $\Delta$ is either
an equilateral triangle, a $45-45-90$ triangle a $30-60-90$, triangle or a
rectangle.
