We measure the thermal conductivity of silicon phononic crystals with asymmetric holes at room and liquid helium temperatures and study the effect of thermal rectification, phonon boundary scattering, neck transmission, and hole positioning. Also, we compare the influence of asymmetric holes on thermal conductivity reduction with the one of conventional circular holes. This reduction is almost 40% larger in the case of pacman shaped holes as compared with circular ones for the same parameters of phononic crystals. Our experimental results can be used to significantly improve the efficiency of thermoelectric devices by using pacman-shaped holes in phononic crystals.