  For a finite planar graph, it associates with some metric spaces, called
(regular) spherical polyhedral surfaces, by replacing faces with regular
spherical polygons in the unit sphere and gluing them edge-to-edge. We consider
the class of planar graphs which admit spherical polyhedral surfaces with the
curvature bounded below by 1 in the sense of Alexandrov, i.e. the total angle
at each vertex is at most $2\pi$. We classify all spherical tilings with
regular spherical polygons, i.e. total angles at vertices are exactly $2\pi$.
We prove that for any graph in this class which does not admit a spherical
tiling, the area of the associated spherical polyhedral surface with the
curvature bounded below by 1 is at most $4\pi - \epsilon_0$ for some
$\epsilon_0 > 0$. That is, we obtain a definite gap between the area of such a
surface and that of the unit sphere.
