We re-examine the existence and extent of the planar structure in the local
galaxy density field, the so-called supergalactic plane (SGP). This struct
ure 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 20 h(-1) Mpc and diameter 80 Mpc aligned with the stand
ard de Vaucouleurs supergalactic coordinates is delta(sgp)similar to 0.5 fo
r both ORS and IRAS. The structure of the SGP is not well described by a ho
mogeneous ellipsoid, although it does appear to be a flattened structure, w
hich we quantify by calculating the moment of inertia tensor of the density
field. The directions of the principal axes vary with radius, but the mino
r axis remains within theta(z)similar to 30 degrees of the standard SGP Z-a
xis, out to a radius of 80 h(-1) Mpc, for both ORS and IRAS. However, the s
tructure changes shape with radius, varying between a flattened pancake and
a dumbbell, the latter at a radius of similar to 50 h(-1) Mpc, where the G
reat Attractor and Perseus-Pisces superclusters dominate the distribution.
This calls to question the connectivity of the 'plane' beyond similar to 40
h(-1) Mpc. 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, yiel
ds a similar misalignment angle and behaviour of axes. The background-indep
endent statistic of axes proposed here can be best used for testing cosmolo
gical models by comparison with N-body simulations.