- For a long time, light manipulation at the nanoscale has been provided primarily with plasmonic materials. However, recent works show that the light can be controlled with dielectric particles. Here, we exploit the asymmetric shape of silicon nanopyramids to control the far-field scattering pattern and the electric field concentration inside the particles by simply changing the incident light polarization. This effect is considered both in air and lossless optical medium. For an explanation of the demonstrated features, we apply the multipole analysis of the scattering cross sections. We show that the electric and magnetic quadrupole resonances can be switched between them by changing the incident wave polarization providing changes of the scattering diagrams. We also show that the polarization control of the scattering properties of pyramidal nanoparticles strongly depends on the refractive index of the surrounding medium. The obtained results can be used for the development of optical antennas, switchers, and polarization filters composed of silicon materials.