  We derive probability density functions for the projected axial ratios of the
real and mock 2PIGG galaxy groups, and use this data to investigate the
intrinsic three dimensional shape of the dark matter ellipsoids that they
trace. As well as analysing the raw data for groups of varying multiplicities,
a convolution corrected form of the data is also considered which weights the
probability density function according to the results of multiple Monte-Carlo
realizations of discrete samples from the input spatial distributions. The
important effect observed is that the best fit distribution for all the raw
data is a prolate ellipsoid with a Gaussian distribution of axial ratios with
$\bar{\beta}=0.36$ and $\sigma=0.14$, whilst for the convolved data the best
fit solution is that of an oblate ellipsoid $\bar{\beta}=0.22$ and
$\sigma=0.1$. Previously only prolate distributions were thought compatible
with the data, this being interprated as evidence of filamentary collapse at
nodes. We also find that even after allowing for the sampling effects, the
corrected data is better fit using separate multiplicity bins, which display a
trend towards more spherical halos in higher multiplicity groups. Finally, we
find that all results in the real data are in good agreement with the mock data
from $\Lambda$CDM simulations, KS tests showing that all comparative data have
been drawn from the same distributions within the $1\sigma$ confidence limits.
