Distribution of quads in the space of relative image angles. Here, a 2D projection of that 3D space is used. The Fundamental Surface of Quads is the horizontal line at Δθ₂₃ = 0. Galaxy-scale quads from Woldesenbet & Williams (2012) are shown as black circles with errorbars. The three quads of B0128 are represented by green squares, labeled with the corresponding subcomponent number. The orange points are quads from a synthetic lens, plotted here for reference, with projected density profile ∝r^−0.8, ellipticity ϵ = 0.25, and external shear γ = 0.25, which is misaligned with the ellipticity position angle by 80°.