What symmetry does the polar curve #r = 3sin3θ# have?
Symmetrical about the pole and, also, #theta = pi/6, theta = (5pi)/6 and theta = (3pi)/2, and also, the radial lines bisecting the angles between these lines..
This is a rose curve with three petals that are 3 units long.
The equispaced lines of symmetry of these petals are
I think I have exhausted all possibilities, in search of symmetry....