We present a new method – called HINORA (HIgh-NOise RANdom SAmple Consensus) – for the identification of regular structures in 3D point distributions. Motivated by the possible existence of the so-called Council of Giants, that is, a ring of 12 massive galaxies surrounding the Local Group in the Local Sheet with a radius of 3.75 Mpc, we apply HINORA to the Local Volume Galaxy catalogue confirming its existence. When varying the lower limit of K-band luminosity of the galaxy entering the catalogue, we further report on the existence of another ring-like structure in the Local Volume that now contains the Milky Way and M31. However, this newly found structure is dominated by low-mass (satellite) galaxies. While we here simply present the novel method as well as its first application to observational data, follow-up work using numerical simulations of cosmic structure formation shall shed light into the origin of such regular patterns in the galaxy distribution. Further, the method is equally suited to identify similar (or even different) structures in various kinds of astrophysical data (e.g. locating the actual ‘baryonic-acoustic oscillation spheres’ in galaxy redshift surveys).