  We show that large spin fermions have very rich spin structures. The local
spin order of a spin-$f$ Fermi gas is a linear combination of $2f$
(particle-hole) angular momentum states, $L=1,..,2f$. $L=1, 2$ represent
ferromagnetic and nematic spin order, while $L\geq 3$ are higher spin orders
that has no analog in spin-1/2 systems. Each $L$ spin sector is characterized
as $L$ pairs of antipodal points on a sphere. Model calculations show that some
of these spin-orders have the symmetry of Platonic solid, and many of them have
non-abelian line defects.
