To increase range and frequency of complete gaps, we construct a model with a matrix-based material (polyethylene) reinforced by a coated cylinder. It is seen in Fig 3(a) that there are no complete gaps, though the dispersion structure is different with Fig 2(a). However, in comparison of Fig 3(b) and Fig 2(b), band gaps at 5100~8000Hz and 8500~10000Hz are observed for the case with 1cm coating, much wider and higher compared to the non-coated hexagonal crystals.