  A periodic orbit on a frictionless billiard table is a piecewise linear path
of a billiard ball that begins and ends at the same point with the same angle
of incidence. The period of a primitive periodic orbit is the number of times
the ball strikes a side of the table as it traverses its trajectory exactly
once. In this paper we find and classify the periodic orbits on a billiard
table in the shape of a 120-isosceles triangle, a 60-rhombus, a 60-90-120-kite,
and a 30-right triangle. In each case, we use the edge tessellation (also known
as tiling) of the plane generated by the figure to unfold a periodic orbit into
a straight line segment and to derive a formula for its period in terms of the
initial angle and initial position.
