  We re-examine the existence and extent of the planar structure in the local
galaxy density field, the so-called Supergalactic Plane (SGP). This structure
is studied here in three dimensions using both the new Optical Redshift Survey
(ORS) and the IRAS 1.2 Jy redshift survey. The density contrast in a slab of
thickness of 20 Mpc/h and diameter of 80 Mpc/h aligned with the standard de
Vaucouleurs' Supergalactic coordinates, is delta_sgp =0.5 for both ORS and
IRAS. The structure of the SGP is not well described by a homogeneous
ellipsoid, although it does appear to be a flattened structure, which we
quantify by calculating the moment of inertia tensor of the density field. The
directions of the principal axes vary with radius, but the minor axis remains
within 30 deg of the standard SGP Z-axis, out to a radius of 80 Mpc/h, for both
ORS and \iras. However, the structure changes shape with radius, varying
between a flattened pancake and a dumbbell, the latter at a radius of ~50
Mpc/h, where the Great Attractor and Perseus-Pisces superclusters dominate the
distribution. This calls to question the connectivity of the `plane' beyond ~40
Mpc/h. The configuration found here can be viewed as part of a web of filaments
and sheets, rather than as an isolated pancake-like structure. An optimal
minimum variance reconstruction of the density field using Wiener filtering
which corrects for both redshift distortion and shot noise, yields a similar
misalignment angle and behaviour of axes. The background-independent statistic
of axes proposed here can be best used for testing cosmological models by
comparison with N-body simulations.
