There's something wrong with the cartesian equation for scarabaeus [1].

I think it should be:

(x^2+y^2) * (x^2+y^2+bx)^2 - a^2 (x^2-y^2)^2 = 0

Also the plot images seem inverted (reflected) along y axis. See plot of the above function in desmos [2].

1. https://www.2dcurves.com/sextic/sexticsc.html

2. https://www.desmos.com/calculator/esrche1qtv