  The peculiar metallic electronic states observed in the Kondo insulator,
samarium hexaboride (SmB$_6$), has stimulated considerable attention among
those studying non-trivial electronic phenomena. However, experimental studies
of these states have led to controversial conclusions mainly to the difficulty
and inhomogeneity of the SmB$_6$ crystal surface. Here, we show the detailed
electronic structure of SmB$_6$ with angle-resolved photoelectron spectroscopy
measurements of the three-fold (111) surface where only two inequivalent
time-reversal-invariant momenta (TRIM) exist. We observe the metallic
two-dimensional state was dispersed across the bulk Kondo gap. Its helical
in-plane spin polarisation around the surface TRIM suggests that SmB$_6$ is
topologically non-trivial, according to the topological classification theory
for weakly correlated systems. Based on these results, we propose a simple
picture of the controversial topological classification of SmB$_6$.
