  Lattices that can be represented in a kagome-like form are shown to satisfy a
universal percolation criticality condition, expressed as a relation between
P_3, the probability that all three vertices in the triangle connect, and P_0,
the probability that none connect. A linear approximation for P_3(P_0) is
derived and appears to provide a rigorous upper bound for critical thresholds.
A numerically determined relation for P_3(P_0) gives thresholds for the kagome,
site-bond honeycomb, (3-12^2), and "stack-of-triangle" lattices that compare
favorably with numerical results.
