Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type

Let $f(\mathbf z,\bar{\mathbf z})$ be a convenient Newton non-degenerate mixed polynomial with strongly polar non-negative weighted homogeneous face functions. We consider regular simplicial cone subdivision $\Sigma^*$ which is admissible for $f$ and take the toric modification $\hat{\pi} : X \to \mathbb{C}^n$ associated $\Sigma^*$. show that resolves topologically singularity of hypersurface germ defined by under Assumption(*) (Theorem 32). This result an extension first part Theorem 11 ([4]) M. Oka, studies positive cases, to cases. also some typical examples (§9).