  In $F(4)$ gauged supergravity in six dimensions, we study supersymmetric
$AdS_6$ black holes with various horizon geometries. We find a new
$AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizon
solution with $\mathfrak{g}_1>1$ and $\mathfrak{g}_2>1$, and present the black
hole solution numerically. The full black hole is an interpolating geometry
between the asymptotically $AdS_6$ boundary and the
$AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizon.
We calculate the Bekenstein-Hawking entropy of the black hole and find a match
with the recently calculated topologically twisted index of 5d $USp(2N)$ gauge
theory on $\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}\times{S}^1$ in
the large $N$ limit. We also find black hole horizons of K\"ahler four-cycles
in Calabi-Yau fourfolds and on Cayley four-cycles in $Spin(7)$ manifolds.
