  In this paper we consider spinor Bose-Einstein condensates with spin f=5 and
f=6 in the presence and absence of external magnetic field at the mean field
level. We calculate all of so-called inert-states of these systems.
Inert-states are very unique class of stationary states because they remain
stationary while Hamiltonian parameters change. Their existence comes from
Michel's theorem. For illustration of symmetry properties of the inert-states
we use method that allows classification of the systems as a polyhedron with 2f
vertices proposed by R. Barnett et al., Phys. Rev. Lett. 97, 180412 (2006).
