  We extend our earlier work on ambipolar diffusion induced formation of
protostellar cores in isothermal sheet-like magnetic interstellar clouds, by
studying nonaxisymmetric collapse for the physically interesting regime of
magnetically critical and supercritical model clouds ($\mui \geq 1$, where
$\mui$ is the initial mass-to-magnetic flux ratio in units of the critical
value for gravitational collapse). Cores that form in model simulations are
effectively triaxial, with shapes that are typically closer to being oblate,
rather than prolate. Infall velocities in the critical model ($\mui = 1$) are
subsonic; in contrast, a supercritical model ($\mui = 2$) has extended
supersonic infall that may be excluded by observations. For the magnetically
critical model, ambipolar diffusion forms cores that are supercritical ($\muc >
1$) and embedded within subcritical envelopes ($\muenv < 1$). Cores in our
models have density profiles that eventually merge into a near-uniform
background, which is suggestive of observed properties of cloud cores.
