  We demonstrate feedback cooling of all the angular motions of a
near-spherical neutral nanoparticle with all the translational motions
feedback-cooled to near the ground state. The occupation numbers of the three
translational motions are $6 \pm 1$, $6 \pm 1$, and $0.69 \pm 0.18$. A tight,
anisotropic optical confinement allows us to clearly observe three angular
oscillations and to identify the ratio of two radii to the longest radius with
a precision of $\unit[0.09]{\%}$. We develop a thermometry for three angular
oscillations and realize feedback cooling of them to temperatures of lower than
$\unit[0.03]{K}$ by electrically controlling the electric dipole moment of the
nanoparticle. Our work not only paves the way to precisely characterize trapped
nanoparticles, but also forms the basis of utilizing them for acceleration
sensing and for exploring quantum mechanical behaviors with both their
translational and rotational degrees of freedom.
