  A class of long gamma-ray bursts (GRBs) with a plateau phase in their X-ray
afterglows obeys a three-dimensional (3D) relation (Dainotti et al. 2016),
between the rest-frame time at the end of the plateau, Ta, its corresponding
X-ray luminosity, La, and the peak luminosity in the prompt emission, Lpeak. We
extended the original analysis with X-ray data from July 2014 to July 2016
achieving a total sample of 183 Swift GRBs with afterglow plateaus and known
redshifts. We added the most recent GRBs to the previous 'gold sample' (now
including 45 GRBs) and obtained a relation plane with intrinsic scatter
compatible within one sigma with the previous result. We compared several GRB
categories, such as short with extended emission, X-ray Flashes, GRBs
associated with SNe, long-duration GRBs, and the gold sample, composed only by
GRBs with light curves with good data coverage and relatively flat plateaus and
evaluated their relation planes. We found that they are not statistically
different from the fundamental plane derived from the gold sample and that the
fundamental plane still has the smallest scatter. We compared the jet opening
angles tabulated in literature with the angles derived using the Eiso-Egamma
relation of the method in Pescalli et al. (2015) and calculated the relation
plane for a sample of long GRBs accounting for the different jet opening
angles. We observed that this correction does not significantly reduce the
scatter. In an extended analysis, we found that the fundamental plane is
independent from several prompt and afterglow parameters.
