Predictions of bond percolation thresholds for the kagom\'e and Archimedean $(3,{12}^2)$ lattices

Here we show how the recent exact determination of the bond percolation threshold for the martini lattice can be used to provide approximations to the unsolved kagom'e and (3,12^2) lattices. We present two different methods, one of which provides an approximation to the inhomogeneous kagom'e and (3,12^2) bond problems, and the other gives estimates of $p_c$ for the homogeneous kagom'e (0.5244088…) and (3,12^2) (0.7404212…) problems that respectively agree with numerical results to five and six significant figures.