Branes wrapped on quadrilaterals

We construct new families of supersymmetric AdS₂₄ solutions of D=6 gauged supergravity and AdS₃₄ solutions of D=7 gauged supergravity, where M₄ are four-dimensional toric orbifolds with four fixed points. These are presented in a unified fashion, that highlights the common underlying geometry of the two families. The D=6 solutions uplift to massive type IIA and describe the near-horizon limit of D4-branes wrapped on M₄, while the D=7 solutions uplift to D=11 supergravity and describe the near-horizon limit of M5-branes wrapped on M₄. We reproduce the entropy and gravitational central charge of the two families by extremizing a function constructed gluing the orbifold gravitational blocks proposed in arXiv: 2210. 16128.