  A statistical survey of spectral anisotropy of space plasma turbulence is
performed using five years measurements from MMS in the magnetosheath. By
measuring the five-point second-order structure functions of the magnetic
field, we have for the first time quantified the three-dimensional anisotropies
and scalings at sub-ion-scales ($<$ 100 km). In the local reference frame
$(\hat L_{\perp}, \hat l_{\perp}, \hat l_{\parallel})$ defined with respect to
local mean magnetic field $\boldsymbol {B}_0$ (Chen et al. 2012), the
"statistical eddies" are found to be mostly elongated along $\boldsymbol {B}_0$
and shortened in the direction perpendicular to both $\boldsymbol {B}_0$ and
local field fluctuations. From several $d_i$ (ion inertial length) toward
$\sim$ 0.05 $d_i$, the ratio between eddies' parallel and perpendicular lengths
features a trend of rise then fall, whereas the anisotropy in the perpendicular
plane appears scale-invariant. Specifically, the anisotropy relations for the
total magnetic field at 0.1-1.0 $d_i$ are obtained as $l_{\parallel} \simeq
2.44 \cdot l_{\perp}^{0.71}$, and $L_{\perp} \simeq 1.58 \cdot
l_{\perp}^{1.08}$, respectively. Our results provide new observational evidence
to compare with phenomenological models and numerical simulations, which may
help to better understand the nature of kinetic scale turbulence.
