  Motivated by experiments on the double perovskites La2ZnIrO6 and La2MgIrO6,
we study the magnetism of spin-orbit coupled j=1/2 iridium moments on the
three-dimensional, geometrically frustrated, face-centered cubic lattice. The
symmetry-allowed nearest-neighbor interaction includes Heisenberg, Kitaev, and
symmetric off-diagonal exchange. A Luttinger-Tisza analysis shows a rich
variety of orders, including collinear A-type antiferromagnetism, stripe order
with moments along the [111]-direction, and incommensurate non-coplanar
spirals, and we use Monte Carlo simulations to determine their magnetic
ordering temperatures. We argue that existing thermodynamic data on these
iridates underscores the presence of a dominant Kitaev exchange, and also
suggest a resolution to the puzzle of why La2ZnIrO6 exhibits `weak'
ferromagnetism, but La2MgIrO6 does not.
