  A K3-surface is a (smooth) surface which is simply connected and has trivial
canonical bundle. In these notes we investigate three particular pencils of
K3-surfaces with maximal Picard number. More precisely the general member in
each pencil has Picard number 19 and each pencil contains four surfaces with
Picard number 20. These surfaces are obtained as the minimal resolution of
quotients X/G, where $G\subset SO(4,\R)$ is some finite subgroup and $X\subset
\P_3(\C)$ denotes a G-invariant surface. The singularities of X/G come from fix
points of G on X or from singularities of X. In any case the singularities on
X/G are A-D-E surface singularities. The rational curves which resolve them and
some extra 2-divisible sets, resp. 3-divisible sets of rational curves generate
the Neron-Severi group of the minimal resolution.
