  Theories of gravity based on teleparallel geometries are characterized by the
torsion, which is a function of the coframe, derivatives of the coframe, and a
zero curvature and metric compatible spin connection. The appropriate notion of
a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the
importance of the de Sitter geometry and Einstein spaces within general
relativity, we shall describe teleparallel de Sitter geometries and discuss
their possible generalizations. In particular, we shall analyse a class of
Einstein teleparallel geometries which have a 4-dimensional Lie algebra of
affine symmetries, and display two one-parameter families of explicit exact
solutions.
