  We find exact solutions for f (T) teleparallel gravity for the cases of
spherically and cylindrically symmetric tetrads. The adopted method is based on
the search for Noether symmetries of point-like Lagrangians defined in Jordan
and Einstein frames. Constants of motion are used to reduce the dynamical
system.We first consider the Lagrangian defined in the Jordan frame for a
spherically symmetric tetrad and, by the help of two constants of motion, we
eliminate a tetrad potential and integrate the other. The more complicated
structure in the Einstein frame is also overcome by the same method. After that
we obtain the Jordan frame Lagrangian for a general cylindrically symmetric
tetrad. Following the same procedure adopted in the spherically symmetric case,
we again obtain the tetrad potentials and then the exact solutions.
