Is there a (fundamental) solution of the laplace equation which is not radial?

Question

In the approach given to solve the laplace equation ( With reference to PDE by L Evans ), we first observe that the laplace operator is rotation invariant .i.e., if we rotate the solution ,it still remains a solution. Then, we narrow down by looking for radial functions ( which remain the same after rotation ) and obtain the fundamental solution.

So, my question is:

Is there a (fundamental) solution of the laplace equation which is not radial ?

Answer 1

Pick any radial solution and add to it any any harmonic function which is not radial.