Detectability of the halo connected 3PCF (upper panels) and reduced 3PCF (lower panels) as a function of the triangle shape. The results are reported at z = 0 and for M_ν = 0.4 eV. The triangle shapes are determined by the side ratios s₁₂/s₂₃ and s₁₃/s₂₃, with s₁₂ ≤ s₁₃ ≤ s₂₃. In each panel, each pixel represents a given triangle shape, where the color shows the absolute value of the detectability averaged over all the triangles available in the all-scales approach with that shape and different sizes. As shown in the legend in the upper right panel, the bottom center, upper right, and upper left parts of the plot contain folded, equilateral, and squeezed triangles, respectively. The dotted curve in the lower right panel marks the location of right-angled triangles. The white region corresponds to the area in the parameter space where it is not possible to obtain a closed triangle. The various columns differ by the range of s₂₃ considered, specified in the intervals shown in the bottom right corner (in units of h⁻¹ Mpc). Empty bins are colored in gray.