We construct infinite new classes of $AdS_4times S^1times S^5$ solutions of type IIB string theory which have non-trivial $SL(2,mathbb{Z})$ monodromy along the $S^1$ direction. The solutions are supersymmetric and holographically dual, generically, to $mathcal{N}=1$ SCFTs in $d=3$. The solutions are first constructed as $AdS_4times mathbb{R}$ solutions in $D=5$ $SO(6)$ gauged supergravity and then uplifted to $D=10$. Unlike the known $AdS_4times mathbb{R}$ S-fold solutions, there is no continuous symmetry associated with the $mathbb{R}$ direction. The solutions all arise as limiting cases of Janus solutions of $d=4$, $mathcal{N}=4$ SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving $mathcal{N}=1,2$ and 4 supersymmetry, as well as a recently constructed $mathcal{N}=1$ $AdS_4times S^1times S^5$ solution (not S-folded). We also present some novel one-sided Janus solutions that are non-singular.
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