  We explore the landscape of F-theory compactifications on Calabi--Yau
fourfolds whose complex structure moduli space is the thrice-punctured sphere.
As a first part, we enumerate all such Calabi--Yau fourfolds under the
additional requirement that it has a large complex structure and conifold point
at two of the punctures. We find 14 monodromy tuples by demanding the monodromy
around infinity to be quasi-unipotent. As second part, we study the four
different types of phases arising at infinity. For each we consider a working
example where we determine the leading periods and other physical couplings. We
also included a notebook that sets up the period vectors for any of these
models.
