$n \mathbb{T} = \mathbb{T} \# \mathbb{T}\# \cdots \# \mathbb{T} =$ a sphere with $n$ handles (connected sum of $n$ tori $\mathbb{T}$)

If we encircle a wire frame cube with a small tube, we get a connected sum of how many tori $\mathbb{T}$?

What about if we do the same thing to a tetrahedron and a dodecahedron?