The intrinsic shape and orientation of the elliptical galaxy NGC 3379 are estimated by dynamical modeling. The maximal ignorance shape estimate, an average over the parameter space, is axisymmetric and oblate in the inner parts, with an outward triaxiality gradient. The 1 sigma limits on total-mass triaxiality T are T < 0.13 at 0.33 kpc and T = 0.08 +/- 0.07 at 3.5 kpc from the center. The luminous short-to-long axis ratio c_L = 0.79 +0.05-0.1 inside 0.82 kpc, flattening to c_L = 0.66 +0.07-0.08 at 1.9 kpc. The results are similar if the galaxy is assumed to rotate about its short axis. Estimates for c_L are robust, but those for T are dependent on whether the internal rotation field is disklike or spheroid-like. Short-axis inclinations between 30 and 50 degrees are preferred for nearly axisymmetric models; but triaxial models in high inclination are also allowed, which can affect central black hole mass estimates. The available constraints on orientation rule out the possibility that the nuclear dust ring at R = 1.5 is in a stable equilibrium in one of the galaxys principal planes. The ring is thus a decoupled nuclear component not linked to the main body of the galaxy. It may be connected with ionized gas that extends to larger radii, since the projected gas rotation axis is near the minor axis of the ring. The gas and dust may both be part of a strongly warped disk; however, if caused by differential precession, the warp will wind up on itself in a few 10^7 years. The decoupling with the stellar component suggests that the gas has an external origin, but no obvious source is present.
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