Branes wrapped on quadrilaterals

We construct new families of supersymmetric AdS${}_2\times {\mathbb{M}}_4$ solutions of $D=6$ gauged supergravity and AdS${}_3\times {\mathbb{M}}_4$ solutions of $D=7$ gauged supergravity, where ${\mathbb{M}}_4$ are four-dimensional toric orbifolds with four fixed points. These are presented in a unified fashion, that highlights their common underlying geometry. The $D=6$ solutions uplift to massive type IIA and describe the near-horizon limit of D4-branes wrapped on ${\mathbb{M}}_4$, while the $D=7$ solutions uplift to $D=11$ supergravity and describe the near-horizon limit of M5-branes wrapped on ${\mathbb{M}}_4$. 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.