A triangular non Bravais lattice was designed in this paper, the crystal constructed form dielectric rods in air background can generate a common band gap for both orthogonal polarizations E and H that is called absolute photonic band gap, but the crystal constructed from air circular holes in dielectric matrix can not generate an absolute photonic band gap. The effective long wavelength dielectric constant of this crystal has been calculated using photonic band structure, simultaneously, the results agree with electrostatic theory well.