We experimentally and numerically demonstrate dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region. The results show that only a small number of rows are needed to create a frequency gap in the transmission spectrum, and that the gap position is insensitive to the incident angle. In particular, there is no defect state at the first gap of a dodecagonal quasiperiodic photonic crystal when there is a cavity in the center region, even though the cavity volume is much larger than the square of the wavelength. The decagonal quasiperiodic crystal can offer great possibilities for creating defect states. These quasiperiodic photonic crystals may find some important applications in photoelectric devices.