Ten-dimensional origin of Minkowski vacua in $\mathcal{N}=8$ supergravity

Maximal supergravity in four dimensions admits two inequivalent dyonic gaugings of the group $\mathrm{S}\mathrm{O}(4)\times \mathrm{S}\mathrm{O}(2,2)⋉T^{16}$. Both admit a Minkowski vacuum with residual $$\mathrm{S}\mathrm{O}$(4) \times $\mathrm{S}\mathrm{O}$(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 ${\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{k}}_4\times S^3\times H^3$ geometry. The IIA/IIB truncations are efficiently related by an outer automorphism of $\mathrm{S}\mathrm{L}(4)\subset {\mathrm{E}}_{7(7)}$. As an application, we give an explicit uplift of the moduli of the vacua into a 4-parameter family of ten-dimensional solutions.