  We study the properties of a line junction which separates the surfaces of
two three-dimensional topological insulators. The velocities of the Dirac
electrons on the two surfaces may be unequal and may even have opposite signs.
For a time reversal invariant system, we show that the line junction is
characterized by an arbitrary parameter \alpha which determines the scattering
from the junction. If the surface velocities have the same sign, we show that
there can be edge states which propagate along the line junction with a
velocity and orientation of the spin which depend on \alpha and the ratio of
the velocities. Next, we study what happens if the two surfaces are at an angle
\phi with respect to each other. We study the scattering and differential
conductance through the line junction as functions of \phi and \alpha. We also
find that there are edge states which propagate along the line junction with a
velocity and spin orientation which depend on \phi. Finally, if the surface
velocities have opposite signs, we find that the electrons must transmit into
the two-dimensional interface separating the two topological insulators.
