Abstract
In the present study, we numerically examined the basins of convergence (BoCs) by deploying the well known Newton-Raphson (NR) iterative scheme, associated to the libration points (LPs) (indeed, act as attractors), in the restricted rhomboidal six-body problem (RRSBP). The parametric evolution of the positions of LPs as a function of the value of parameter "b" is illustrated. Additionally, the linear stability of these LPs and the regions of possible motion are also studied. The BoCs, on the configuration (x, y) plane are unveiled by using the bivariate version of NR-iterative method. Further, a systematic analysis is performed in an order to unveil how the parameter "b" affects the topology as well as degree of fractality of the BoCs. We have also recorded the required number of iterations along with the associated probability distributions (PDs) to show how they are related to the regions of convergence. It is observed that the topology of the BoCs is directly linked with the shape of rhombus. Moreover, basin entropy and basin boundary entropy are also evaluated to unveil the degree of uncertainty of the BoC diagram.