  We construct a class of codimension-2 solutions in supergravity that realize
T-folds with arbitrary $O(2,2,\mathbb{Z})$ monodromy and we develop a geometric
point of view in which the monodromy is identified with a product of Dehn
twists of an auxiliary surface $\Sigma$ fibered on a base $\mathcal{B}$. These
defects, that we call T-fects, are identified by the monodromy of the mapping
torus obtained by fibering $\Sigma$ over the boundary of a small disk
encircling a degeneration. We determine all possible local geometries by
solving the corresponding Cauchy-Riemann equations, that imply the equations of
motion for a semi-flat metric ansatz. We discuss the relation with the
F-theoretic approach and we consider a generalization to the T-duality group of
the heterotic theory with a Wilson line.
