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The notion of spacetime symmetry is essential to describe gravitatingphysical systems like planets, stars, black holes, or the universe as a whole,since they possess, at least to good approximation, spherical, axial, orspatially homogeneous and isotropic symmetry, respectively. This article givesa quick overview over the known facts on spacetime symmetries in teleparallelgravity. The most general spherical, axial, or spatially homogeneous andisotropic tetrads in Weitzenb\"ck gauge are presented and a brief discussionabout symmetric solutions of the anti-symmetric field equations in$f(T,B,\phi,X)$-gravity is given.

A quick guide to spacetime symmetry and symmetric solutions in teleparallel gravity