We study various forms of diagonal tetrads that accommodate Black Hole
    solutions in $f(T)$ gravity with certain symmetries. As is well-known, vacuum
    spherically symmetric diagonal tetrads lead to rather boring cases of constant
    torsion scalars. We extend this statement to other possible horizon topologies,
    namely, spherical, hyperbolic and planar horizons. All such cases are forced to
    have constant torsion scalars to satisfy the anti-symmetric part of the field
    equations. We give a full classification of possible vacuum static solutions of
    this sort. Furthermore, we discuss addition of time-dependence in all the above
    cases. We also show that if all the components of a diagonal tetrad depend only
    on one coordinate, then the anti-symmetric part of the field equations is
    automatically satisfied. This result applies to the flat horizon case with
    Cartesian coordinates. For solutions with a planar symmetry (or a flat
    horizon), one can naturally use Cartesian coordinates on the horizon. In this
    case, we show that the presence of matter is required for existence of
    non-trivial solutions. This is a novel and very interesting feature of these
    constructions. We present two new exact solutions, the first is a magnetic
    Black Hole which is the magnetic dual of a known electrically charged Black
    Hole in literature. The second is a dyonic Black Hole with electric and
    magnetic charges. We present some features of these Black holes, namely,
    extremality conditions, mass, behavior of torsion and curvature scalars near
    the singularity.

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