  We construct new supersymmetric $\mathrm{AdS}_2\times \mathbb{M}_4$ solutions
of $D=6$ gauged supergravity, where $\mathbb{M}_4$ are certain four-dimensional
orbifolds. After uplifting to massive type IIA supergravity these correspond to
the near-horizon limit of a system of $N$ D4-branes and $N_f$ D8-branes wrapped
on $\mathbb{M}_4$. In one class of solutions $\mathbb{M}_4 =
\Sigma_{\mathrm{g}}\ltimes\Sigma$ is a spindle fibred over a smooth Riemann
surface of genus $\mathrm{g}>1$, while in another class $\mathbb{M}_4 =
\Sigma\ltimes\Sigma$ is a spindle fibred over another spindle. Both classes can
be thought of as orbifold generalizations of Hirzebruch surfaces and, in the
second case, we describe the solutions in terms of toric geometry. We show that
the entropy associated with these solutions is reproduced by extremizing an
entropy function obtained by gluing gravitational blocks, using a general
recipe for orbifolds that we propose. We also discuss how our prescription can
be used to define an off-shell central charge whose extremization reproduces
the gravitational central charge of analogous $\mathrm{AdS}_3\times
\mathbb{M}_4$ solutions of $D=7$ gauged supergravity, arising from wrapping
M5-branes on $\mathbb{M}_4$.
