Solution
= Solution
For $T^2$, take the unit square $[0,1]\times[0,1]$. Identify
$$
(0,y)\sim(1,y),
\qquad
(x,0)\sim(x,1),
$$
so both pairs of opposite edges have matching directions.
For $K$, take $[0,1]\times[-1/2,1/2]$. Identify
$$
(x,-1/2)\simeq(x,1/2)
$$
with matching directions, and
$$
(0,y)\simeq(1,-y)
$$
with reversed directions. These equations specify the arrows on the two fundamental-domain drawings.