  Koll\'ar gave a series of examples of rational surfaces of Picard number $1$
with ample canonical divisor having cyclic singularities. In this paper, we
construct several series of new examples in a geometric way, i.e., by blowing
up several times inside a configuration of curves on the projective plane and
then by contracting chains of rational curves. One series of our examples have
the same singularities as Koll\'ar's examples.
