  We demonstrate the measurement of nanoparticle shape by angularly resolved
Rayleigh scattering of single optical levitated particles that are oriented in
space via the trapping light in vacuum. This technique is applied to a range of
particle geometries, from perfect spherical nanodroplets to octahedral
nanocrystals. We show that this method can resolve shape differences down to a
few nanometers and be applied in both low-damping environments, as demonstrated
here, and in traditional overdamped fluids used in optical tweezers.
