(Unoriented) T-folds with few T's

We use the combined action of Z(2)-chiral reflections (T-dualities) and shifts to build N = 1, 2 supersymmetric four-dimensional string compactifications with few moduli. In particular, we consider Z(2)(4) asymmetric orbifolds of Type IIB on the maximal torus of SO(12) that mimic N = 2 Calabi-Yau compactifications with small effective Hodge numbers starting from (h(11), h(21)) = (1, 1). We analyze possible unoriented projections, providing Type I examples with or without open strings. N = 1 oriented asymmetric shift-orbifolds of Type IIB with few chiral multiplets are also presented.