The sunflower as originally defined has no symmetry. But if we take the set-union of it with the same thing rotated by j/k of a turn, for each j=1,2,...,k-1, then the resulting point set is (a) k-fold symmetric (b) still obeys my lattice approx theorem (c) still obeys theorems about decrease rate of max gaps and min gaps [if sunflower based on a quadratic irrational angle] and hence "no holes" and "no high density" theorems. Surely some plants like to have symmetry, no? -- Re 4D etc sunflower ideas with quaternions... the combing of 3 kinds of hairs on the surface x^2+y^2+z^2+t^2=1 arises as follows: view the 4 coordinates as a quaternion q with |q|=1, and multiply point q by i, j, and k (on left) to obtain the 3 direction arrows (tangent to the sphere at q), and mutually perpendicular, that are the three colors of "hair." So I suppose some sort of 4D sunflower analogue, point set parameterized by 3 integer parameters a,b,c, would be exp(i*a*g1+j*b*g2+k*c*g3) * (a^2+b^2+c^2)^(3/8) using quaternion exponentiation where g1,g2,g3 are three suitable quadratic irrationals. More generally still the argument of the exp() would be g1*a+g2*b+g3*c where now g1,g2,g3 are suitable irrational pure-imaginary quaternion constants such exp()=1 is ONLY possible if a=b=c=0. One can similarly make an 8D sunflower analogue using octonions.