  The fragmentation of molecular cloud cores a factor of 1.1 denser than the
critical Bonnor-Ebert sphere is examined though three-dimensional numerical
simulations. A nested grid is employed to resolve fine structure down to 1 AU
while following the entire structure of the molecular cloud core of radius 0.14
pc. A total of 225 models are shown to survey the effects of initial rotation
speed, rotation law, and amplitude of bar mode perturbation. The simulations
show that the cloud fragments whenever the cloud rotates sufficiently slowly to
allow collapse but fast enough to form a disk before first-core formation. The
latter condition is equivalent to $\Omega_0 t_{\rm ff} \gtrsim 0.05$, where
$\Omega_0$ and $t_{\rm ff}$ denote the initial central angular velocity and the
freefall time measured from the central density, respectively. Fragmentation is
classified into six types: disk-bar, ring-bar, satellite, bar, ring, and
dumbbell types according to the morphology of collapse and fragmentation. When
the outward decrease in initial angular velocity is more steep, the cloud
deforms from spherical at an early stage. The cloud deforms into a ring only
when the bar mode m = 2 perturbation is very minor. The ring fragments into two
or three fragments via ring-bar type fragmentation and into at least three
fragments via ring type fragmentation. When the bar mode is significant, the
cloud fragments into two fragments via either bar or dumbbell type
fragmentation. These fragments eventually merge due to their low angular
momenta, after which several new fragments form around the merged fragment via
satellite type fragmentation.
