  In this paper, we measure the ellipticities of 30 LSB dI galaxies and compare
the ellipticity distribution with that of 80 dEs (Ryden & Terndrup 1994; Ryden
et al. 1998) and 62 BCDs (Sung et al. 1998). We find that the ellipticity
distribution of LSB dIs is very similar to that of BCDs, and marginally
different from that of dEs. We then determine the distribution of intrinsic
shapes of dI galaxies and compare to those of other type dwarf galaxies under
various assumptions. First, we assume that LSB dIs are either all oblate or all
prolate, and use non-parametric analysis to find the best-fitting distribution
of intrinsic shapes. With this assumption, we find that the scarcity of nearly
circular LSB dIs implies, at the 99% confidence level, that they cannot be a
population of randomly oriented oblate or prolate objects. Next, we assume that
dIs are triaxial, and use parametric analysis to find permissible distributions
of intrinsic shapes. We find that if the intrinsic axis ratios, $\beta$ and
$\gamma$, are distributed according to a Gaussian with means $\beta_0$ and
$\gamma_0$ and a common standard deviation of $\sigma$, the best-fitting set of
parameters for LSB dIs is $(\beta_0,\gamma_0,\sigma) = (0.66,0.50,0.15)$, and
the best fit for BCDs is $(\beta_0,\gamma_0,\sigma) = (0.66,0.55,0.16)$, while
the best fit for dEs is $(\beta_0,\gamma_0,\sigma) = (0.78,0.69,0.24)$. The dIs
and BCDs thus have a very similar shape distribution, given this triaxial
hypothesis, while the dEs peak at a somewhat more spherical shape. Our results
are consistent with an evolutionary scenario in which the three types of dwarf
galaxy have a close relation with each other.
