  We construct $AdS_4 \times \Sigma$ and $AdS_2 \times \Sigma \times \Sigma_g$
solutions in F(4) gauged supergravity in six dimensions, where $\Sigma$ is a
two dimensional manifold of non-constant curvature with conical singularities
at its two poles, called a spindle, and $\Sigma_g$ is a constant curvature
Riemann surface of genus g. We find that the first solution realizes a
"topologically topological twist", while the second class of solutions gives
rise to an "anti twist". We compute the holographic free energy of the $AdS_4
\times \Sigma$ solution and find that it matches the entropy computed by
extremizing an entropy functional that is constructed by gluing gravitational
blocks. For the $AdS_2 \times \Sigma \times \Sigma_g$ solution, we find that
the Bekenstein-Hawking entropy is reproduced by extremizing an appropriately
defined entropy functional, which leads us to conjecture that this solution is
dual to a three dimensional SCFT on a spindle. A class of the $AdS_2 \times
\Sigma \times \Sigma_g$ solutions can be embedded in four dimensional T3 gauged
supergravity, which is a subtruncation of the six dimensional theory.
