  Polar-ring galaxies (PRGs) are fascinating systems in which the central
object (typically, an early-type galaxy) is encircled by a large-scale ring of
stars, gas, and dust with almost perpendicular spin. PRGs are rare objects and
their formation mechanism is not entirely clear. In this paper, we present a
new sample of 31 candidates to PRGs identified in the Sloan Digital Sky Survey
(SDSS). Using their stacked $gri$ images, we determined geometrical parameters
of these galaxies (the position angle and the size of the host galaxy and the
ring). We compare our sample objects to the previously known PRGs and discuss
their general characteristics (the frequency of faint outer structures, the
luminosity--size relation, and the distribution by the apparent angle between
the ring and the host galaxy). Our main results are: (i) Central galaxies of
PRGs follow the luminosity--size relation for ordinary galaxies. The ring
components are located along the similar relation but with a larger scatter.
This increasing scatter may be the result of a secondary origin of polar
structures. (ii) At least half of PRGs show a ring component within 20$^\circ$
from the perpendicular orientation.
