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Lattices that can be represented in a kagome-like form are shown to satisfy auniversal percolation criticality condition, expressed as a relation betweenP_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) isderived 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 comparefavorably with numerical results.

Universal condition for critical percolation thresholds of kagome-like lattices