Epicycloid To obtain an epicycloid with n number of cusps, let r2 = r1/n the outer limit of the graph ist r1+2xr2 in order to calculate the number of turns until the pattern of the graph repeats itself: reduce the fraction of r1/r2 to lowest terms. i.e. find the greatest common divisor and divide r1 and r2 by it. Then, r2 ist the number of turns. Web: http://xahlee.org/SpecialPlaneCurves_dir/EpiHypocycloid_dir/epiHypocycloid.html