This started when i was wondering why p-orbitals have an unsymmetrical shape (which isn't clear to me yet). But then i came across Halliday/Resnick/Walker's Fundamentals of Physics. In it, they have said that the three p-orbitals show their individual shapes in presence of a magnetic field. But normally, in an isolated atom, the three p-orbitals have the same energy and are indistinguishable, and that their combined probability density is spherically symmetrical.
I am having trouble in visualizing this. The three dumbells do not look like they could complete a sphere! For example, what about the region in the direction of $\hat i + \hat j + \hat k$? Wouldn't gaps be left behind? Wouldn't this destroy the symmetry of the distribution?
A visual graph of the three separately and then the three together (like different coloured dots for different p-orbitals) would help. I have no resources or skills (not even remotely close!) to do it myself, so i am requesting this to the skilled people out here. Thank you very much!