  In this paper we model and analyse the B-V/V-K radial color gradients
observed in the Cartwheel ring galaxy. Along with the color-color diagrams, we
use the Q_BVK combined color indices, which minimise the uncertainties in the
observed B-V and V-K colors introduced by dust extinction. To model the optical
and near-infrared color properties of the Cartwheel galaxy, we assume that an
intruder galaxy generates an expanding ring density wave in the Cartwheel's
disk, which in its turn triggers massive star formation along the wave's
perimeter according to the Schmidt law. We use the population synthesis to
calculate the color properties of stellar populations formed in the expanding
density wave. The results of color modelling suggest that the pre-collision
Cartwheel was a late-type spiral, embedded in an extensive gaseous disk of
sub-critical surface density. The properties of the old stellar disk are
typical for the late-type Freeman disks, with the central surface brightness in
V-band and the scale length being 21.0 mag arcsec^-2 and 2 kpc respectively.
The pre-collision gaseous disk has a metallicity gradient ranging from
z=z_sun/5 at the outer regions to z=z_sun in the central regions. At present,
the wave of star formation has passed the initial extent of the pre-collision,
old stellar disk and is currently moving in the predominantly gaseous,
low-metallicity disk at the radius of 16 kpc. Neither young stellar populations
formed in an expanding density wave, nor their mixture with the old,
pre-collision stellar populations can reproduce the B-V and V-K colors of the
Cartwheel's nucleus+inner ring. We find that an additional 10-Myr-old burst of
star formation in the nuclear regions, along with the visual extinction of 1.3
mag, might be responsible for the peculiar colors of the Cartwheel's nucleus.
