  The 'rigid unit mode' (RUM) model requires unit blocks, in our case
tetrahedra of SiO_4 groups, to be rigid within first order of the displacements
of the O-ions. The wave-vectors of the lattice vibrations, which obey this
rigidity, are determined analytically. Lattices with inversion symmetry yield
generically surfaces of RUMs in reciprocal space, whereas lattices without this
symmetry yield generically lines of RUMs. Only in exceptional cases as in
beta-quartz a surface of RUMs appears, if inversion symmetry is lacking. The
occurence of planes and bending surfaces, straight and bent lines is discussed.
Explicit calculations are performed for five modifications of SiO_2 crystals.
