  For a hyperplane $H$ supporting a convex body $C$ in the hyperbolic space
$\mathbb{H}^d$ we define the width of $C$ determined by $H$ as the distance
between $H$ and a most distant ultraparallel hyperplane supporting $C$. The
minimum width of $C$ over all supporting $H$ is called the thickness $\Delta
(C)$ of $C$. A convex body $R \subset \mathbb{H}^d$ is said to be reduced if
$\Delta (Z) < \Delta (R)$ for every convex body $Z$ properly contained in $R$.
We describe a class of reduced polygons in $\mathbb{H}^2$ and present some
properties of them. In particular, we estimate their diameters in terms of
their thicknesses.
