Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of $1\mu \mathrm{m}$ and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about $1500\mathrm{nm}$ , then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches $0.7\mu \mathrm{m}$ . Finally, the mode Q factors greatly enhance as the hole diameter reaches about $1\mu \mathrm{m}$ . The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor.