VI. SUMMARY Acknowledgment 22 FYW would like to thank Professor Z. G. Zheng for the hospitality at the Beijing Normal University. WG is much indebted to H. W. J. Bl¨ ote for valuable discussions. We thank R. M. Ziff for valuable comments and sending a copy of Ref. [38] prior to publication. This work is supported by the National Science Foundation of China (NSFC) under Grant No. 10675021, by the Program for New Century Excellent Talents in University (NCET), and by the High Finally, our analysis of critical properties is based on the use of lattice-dependent con- stants A, B, C for the hatched triangles shown in Fig. 1. We have developed an algorithm of evaluating expressions of A, B, C using computers for hatched triangles in the form of a stack-of-triangle structure. We have also computed the critical thresholds for the Potts and bond percolation on the 3- 12 lattice and ( $^{n}$×n ) : ( $^{n}$×n ) kagome-type subnet lattices using the homogeneity assumption (6). To assess the accuracy of our numerical analysis as well as that of the homogeneity assumption, we have applied our numerical procedure to study critical properties of models for which exact results are known. The comparison of numerical and known results shows that the numerical procedure is accurate to 7 or 8 significant digits in determining critical thresholds. Assuming the same degree of accuracy for all lattices, this in turn infers that the homogeneity assumption determines critical threshold with an accuracy up to 5 decimal places or higher. We have studied critical properties of the q -state Potts model and bond and site perco- lation on two general classes of lattices, the triangular-type and kagome-type lattices. For the triangular-type lattices of Fig. 1(a), the exact critical frontier is known and this led to a determination of the exact critical thresholds of site percolation on (1 × 1) : ( $^{n}$× n ) kagome-type subnet lattices. Results for 1 ≤ n ≤ 6 are given. For the kagome-type lattices of Fig. 1(b), no exact results are known except for q = 2. We carried out finite-size analysis to numerically determine critical properties for various lattice models including the 3-12 lat- tice and ( $^{n}$× n ) : ( $^{n}$× n ) kagome-type subnet lattices. Our numerical results on conformal anomaly and magnetic correlation length verify that the principle of universality holds.