  General Teleparallel theories assume that curvature is vanishing in which
case gravity can be solely represented by torsion and/or nonmetricity. Using
differential form language, we express the Riemannian Gauss-Bonnet invariant
concisely in terms of two General Teleparallel Gauss-Bonnet invariants, a bulk
and a boundary one. Both terms are boundary terms in four dimensions. We also
find that the split is not unique and present two possible alternatives. In the
absence of nonmetricity our expressions coincide with the well-known Metric
Teleparallel Gauss-Bonnet invariants for one of the splits. Next, we focus on
the description where only nonmetricity is present and show some examples in
different spacetimes. We finish our discussion by formulating novel modified
Symmetric Teleparallel theories constructed with our new scalars.
