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Diesel Particulate Filter (DPF) requires higher capacity of ash materials, incombustible particulate matters derived from lubricant oil, engine wear, etc., for usage of long lifetime. Conventional DPF such as SiC-DPF has been developed by optimizing cell geometry as of octagonal inlet shapes and square outlet shapes, called as “Octosquare”. Thus-obtained SiC-DPF could improve the lifetime to previous type with square cell design. However, under ash/soot-loading, pressure drop between upstream and downstream DPF, involving in the fuel penalty for the vehicle itself, makes higher. On the other hand, it was previously proposed that aluminum titanate (AT) with hexagonal cell design shows lower pressure drop and higher endurance performance. The characteristic of the filter design consists of higher open frontal area, relating to higher ash capacity, and higher filtration area, enabling lower pressure drop with soot loading.