Schematic of conditions under which Alcyoneus is not only the longest GRG in the plane of the sky but also in three dimensions. Alcyoneus’s inclination angle, θ, is not well determined, and therefore the full range of possibilities is shown on the horizontal axis. To surpass Alcyoneus in true proper length, challengers must have smaller inclination angles than Alcyoneus (i.e. appear below the dotted grey equality line). More specifically, as a function of θ, we show the inclination angle θ_max, c below which challengers with a projected proper length l_p, c > 4 Mpc trump Alcyoneus (coloured curves). The shaded areas of parameter space represent regimes with a particularly straightforward interpretation. One can imagine populating the graph with five points (located along the same vertical line), representing the ground-truth inclination angles of Alcyoneus and its five challengers. If any of these points fall in the red-shaded area, Alcyoneus is not the longest GRG in 3D. If all points fall in the green-shaded area, Alcyoneus is the longest GRG in 3D.