  For a sample of 96,951 galaxies from the Sloan Digital Sky Survey Data
Release 3, we study the distribution of apparent axis ratios as a function of
r-band absolute magnitude and surface brightness profile type. We use the
parameter fracDeV to quantify the profile type (fracDeV = 1 for a de
Vaucouleurs profile; fracDeV = 0 for an exponential profile). When the apparent
axis ratio q_{am} is estimated from the moments of the light distribution, the
roundest galaxies are very bright (M_r \sim -23) de Vaucouleurs galaxies and
the flattest are modestly bright (M_r \sim -18) exponential galaxies. When the
apparent axis ratio q_{25} is estimated from the axis ratio of the 25
mag/arcsec^2 isophote, we find that de Vaucouleurs galaxies are flatter than
exponential galaxies of the same absolute magnitude. For a given surface
brightness profile type, very bright galaxies are rounder, on average, than
fainter galaxies. We deconvolve the distributions of apparent axis ratios to
find the distribution of the intrinsic short-to-long axis ratio gamma, assuming
constant triaxiality T. For all profile types and luminosities, the
distribution of apparent axis ratios is inconsistent with a population of
oblate spheroids, but is usually consistent with a population of prolate
spheroids. Bright galaxies with a de Vaucouleurs profile (M_r < -21.84, fracDeV
> 0.9) have a distribution of q_{am} that is consistent with triaxiality in the
range 0.4 < T < 0.8, with mean intrinsic axis ratio 0.66 < gamma < 0.69. The
fainter de Vaucouleurs galaxies are best fit with prolate spheroids (T = 1)
with mean axis ratio gamma = 0.51.
