“…Several programs (e.g., HaloSim [18] and HaloPoint [19]) using known minimum deviations of sunlight for the given shapes of ice crystals and the relative positions between the Sun and ice crystals are available for such simulations. Previous studies also estimated the geometries of ice crystals based on the angles at which halos were observed, in particular, to explain rarely seen circumscribed halos, such as 91, 181, 201, Scheiner's halo at $281 and 351 [20,21,13,16,17].…”