  I compute the estimated distribution function f(q) for the apparent axis
ratio q of various types of stellar systems, using a nonparametric kernel
method. I then invert f(q) to find the distribution of intrinsic axis ratios,
using two different hypotheses: first, that the stellar systems are all oblate,
and second, that they are all prolate. The shapes of globular clusters in our
own galaxy are consistent, at the 99% confidence level, with both the oblate
and prolate hypothesis. The shapes of dwarf galaxies in the Virgo cluster are
consistent, at the 99% confidence level, with the prolate hypothesis, but
inconsistent with the oblate hypothesis. The shapes of star clusters in the
Large Magellanic Cloud, of ordinary elliptical galaxies, of brightest cluster
ellipticals, and of galaxy clusters are all inconsistent, at the 99% confidence
level, with both the oblate and prolate hypotheses. The globular clusters in
our galaxy are older than their half-mass relaxation time, and are most likely
rotationally flattened oblate spheroids. The other stellar systems considered
are generally younger than their half-mass relaxation time, and thus are
triaxial bodies flattened by anisotropy of their velocity dispersion.
