Interesting... so is photon a particle or a wave? what about for an electron? Your question seems innocent enough, simple and perhaps intuitive... however, your question may not be the 'right' question to ask about quarks (?)
We know that there are THREE quarks for baryons (and TWO for mesons), not because we directly "see" three/two things in experiments, but we can infer that from the effects the target proton causes in an high energy collision experiments (if our experiments were correct, and we believe in the physics as we know it) OK, to cut a long story short (which I am not qualify to tell anyway), it turns out that things are only consistent in these scattering experiments if we assume nucleons are made up of 3 "things" which we called quarks. Now, the accelerators we have today (or even the LHC) do not produce collision with high enough energy that can break quarks down further and hence we believe they are fundamental and perhaps infinitestimally small, ... err.. structureless is probably the better word for it. By the way, there is also a experimental upper bound on their radius, which is very tiny as you may guess... hence we like to refer to them as point-like.
A related issue is of course coming from QM and about the "fuzziness" nature of stuff. like the good old electron cloud. In that spirit alone, it may render your question meaningless.
perhaps, it is our nature to prefer a nice geometric description of things that brings about the concepts of
the Earth is a perfect sphere, NH_3 molecules form exact tetrahedrons,
at the end of the day though they are approximations. If the approximation is very close to being exact, that's great! But there is no guarantee that the same concepts will prevail at the sub-atomic level. We can have a "mathematical" description of them to aid our analysis and perhaps to formalise them. But it is often difficult to visualise them (although more experimental data will help).
The moral of all these is that (and to answer your question) don't take that picture of spherical quarks/nucleans too seriously. As fas as we know and what we can infer, quarks are extremely small, so small that it is meaningless to talk about its shape. As for nucleons, they certainly are composite objects with an effective radius. Now, you may ask how can three infinitestimally small objects combine to give an "extended" object? Hehehehee...
well, to be honest I don't really know the correct answer to that, but I would say, if you have three dots closely packed together but not overlapping in such a way that you only see one dot all the time when you are close-by, then if you move away from it, it looks like one "big" dot... your nucleon.
(perhaps someone can correct or add to this, also not sure whether gluons play a role in this for we know that energy and mass are the essentially the same at relativistic energy)
Anyway, should the nucleon then regarded as spherical? triangular? tetrahedral? oval? I guess the natural choice would be spherical for symmetry reasons and perhaps easier to model its scattering behaviors (ie. billard balls analogy) But then of course nucleons also have different spin/excited states which are modeled by "the Shell model", now I am not sure whether under those situation "the effective shape" of the nucleon can change (like the way the electron cloud changes)... . but then again, we are quite comfortable with the idea of atoms being "spherical" despite the fact that electron orbitals can take on different "shapes".
comments welcomed
