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We apply the dynamical modeling approach of Statler (1994b) to 13 ellipticalgalaxies from the Davies and Birkinshaw (1988) sample of radio galaxies toderive constraints on their intrinsic shapes and orientations. We develop aniterative Bayesian algorithm to combine these results to estimate the parentshape distribution from which the sample was drawn, under the assumption thatthis parent distribution has no preferred orientation. In the process we obtainimproved estimates for the shapes of individual objects. The parent shapedistribution shows a tendency toward bimodality, with peaks at the oblate andprolate limits. Under minimal assumptions about the galaxies' internaldynamics, 35% of the objects would be strongly triaxial (0.2 < T < 0.8).However, the parent distribution is sensitive to the assumed orbit populationsin the galaxies. Dynamical configurations in which all galaxies rotate purelyabout either their long or short axes can be ruled out because they wouldrequire the sample to have a strong orientation bias. Configurations in whichthe mean motion about the short or long axis is either ``disklike''---droppingoff away from the symmetry planes---or ``spheroidlike''---remaining roughlyconstant at a given radius---are equally viable. Spheroidlike rotation in thelong-axis or short-axis tube orbits significantly lowers the abundance ofprolate or oblate galaxies, respectively. If rotation in ellipticals isgenerally disklike, then triaxiality is rare; if spheroidlike, triaxiality iscommon.

The Intrinsic Shape Distribution of a Sample of Elliptical Galaxies