  ESO 566-24 is an extraordinary barred galaxy, which has four regularly spaced
spiral arms in blue light images. This type of four-armed spiral structure,
which is rare among the spiral population, is clearly seen also in
near-infrared images, and thus is present in the old stellar population. We
have constructed dynamical models of ESO 566-24 in order to understand the
cause of its four-armed structure. The disk gravitational potential is
determined from near-infrared photometry, and the gas dynamics is modelled as
inelastically colliding particles. The resulting morphology and kinematics with
different assumed pattern speeds, disk vertical thicknesses and dark halo
contributions is compared with observations. Our models can reproduce the main
morphological features of this galaxy: the four-armed spiral, and the inner and
nuclear rings. The pattern speed of the bar in this galaxy is such that the
corotation resonance is well outside the bar radius, the resonance radius is
1.6 +/- 0.3 times the bar radius. The four-armed spiral resides in the region
between inner and outer 4/1-resonances. Also, the main kinematical features,
including bar-induced deviations from circular rotation, are explained by our
models. The best fit is obtained when the dark halo contribution is just enough
to make the modelled rotation curve match the observed one. This ``minimum
halo'' is rather moderate: luminous matter dominates the rotation curve within
the disk region.
