Ambiguity on determining a relativistic Dirac orbital's "shape" when it has two angular components

[Wikipedia](https://en.wikipedia.org/wiki/Hydrogen-like_atom) says that a relativistic Dirac atomic orbital is a 4-component vector, with two angular parts and two spin parts. It also says, indirectly, that 'the top two components of a 2p(1/2) orbital are not spherical, while the bottom two components are', and vice versa for the 2s(1/2) one. So the 2p(1/2) orbital is both spherical and non-spherical at the same time.


However, it is known that a p(1/2) orbital is completely spherical, a contradiction. This can only happen if only one of the components of the 4-component vector is taken to represent its "shape"; that component is the top two in s(1/2) and the bottom two in p(1/2), and is hence arbitrary.


My question now follows- is there a definite algorithm to "pull out" two of the four components of a Dirac relativistic orbital, to determine the orbital's "shape"? It all seems arbitrary to me...


EDIT: Forgot that I was myself a mathematics undergrad student... maybe it's the dot product of that 4-component vector with itself that's spherical. Is it the case?


