Maximal supergravity in four dimensions admits two inequivalent dyonic gaugings of the group SO(4)×SO(2,2) ⋉T16. Both admit a Minkowski vacuum with residual SO(4)×SO(2)2 symmetry and identical spectrum. We explore these vacua and their deformations. Using exceptional field theory, we show that the four-dimensional theories arise as consistent truncations from IIA and IIB supergravity, respectively, around a Mink4×S3 ×H3 geometry. The IIA/IIB truncations are efficiently related by an outer automorphism of SL(4) ⊂ E7(7). As an application, we give an explicit uplift of the moduli of the vacua into a 4-parameter family of ten-dimensional solutions.