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.