  In this paper we study the shape characteristics of a polymer chain in a good
solvent using a mesoscopic level of modelling. The dissipative particle
dynamics simulations are performed in the $3D$ space at a range of chain
lengths $N$. The scaling laws for the end-to-end distance and gyration radius
are examined first and found to hold for $N\geq 10$ yielding reasonably
accurate value for the Flory exponent $\nu$. Within the same interval of chain
lengths, the asphericity, prolateness, size ratio and other shape
characteristics of the chain are found to become independent of $N$. Their mean
values are found to agree reasonably well with the respective theoretical
results and lattice Monte Carlo simulations. Broad probability distributions
for the shape characteristics are found resembling in form the results of
lattice Monte Carlo simulations. By means of analytic fitting of these
distributions the most probable values for the shape characteristics are found
to supplement their mean values.
