A recent publication [Nature (London) 404, 740 (2000)] claimed that absolute photonic gaps can be realized in 12-fold quasicrystalline arrangement of small airholes in a matrix of silicon nitride or glass. The result is rather surprising since silicon nitride (n=2.02) and in particular, glass (n=1.45) have rather low refractive index. In this work, we have studied the transmission properties of the same systems by using the multiple-scattering method. We found that the 12-fold triangle-square tiling is indeed very good for the realization of photonic gaps and we found absolute gaps in systems with airholes in dielectric, dielectric cylinders in air, and metal cylinders in air. However, for the case of air-holes in a dielectric background, absolute gaps appear only when the dielectric contrast is sufficiently high, and both silicon nitride and glass have refractive indices below the threshold.