  We introduce a family of spaces, parametrized by positive real numbers, that
includes all of the Hirzebruch surfaces. Each space is viewed from two distinct
perspectives. First, as a leaf space of a compact, complex, foliated manifold,
following [BZ1]. Second, as a symplectic cut of the manifold $\mathbb{C}\times
S^2$ in a possibly nonrational direction, following [BP2].
