The band structure of three types of photonic crystals is studied. In these photonic crystals, the rotationally asymmetric V-shaped air holes are combined while changing their orientation. We find that the band structure is very sensitive to the method of combination. From this result, we can say that the periodical perturbation produced only by change of the air-hole orientation can change the band structure largely. This idea can be applied to many apprications such as lasers which have unique beam patterns.