  This paper provides explicit closed formulas in terms of tautological classes
for the cycle classes of the height and Artin invariant strata in families of
K3 surfaces. The proof is uniform for all strata and uses a flag space as the
computations in [arXiv:math/0412272] for the Ekedahl-Oort strata for families
of abelian varieties, but employs a Pieri formula formula to determine the push
down to the base space.
