If you've ever looked at a model of the atom, you'd probably guess that electrons are spherical. But these elementary particles are actually slightly egg-shaped...and proving that could mean trouble for one particular model of subatomic physics.
Now, make no mistake - even if you made an electron big enough to be seen with the naked eye, it would still look almost perfectly spherical. These are very small distortions we're talking about, and because electrons themselves are so very, very small, it's an open question whether we actually have the technology needed to detect these distortions. According to the Standard Model, the egg-shaped distortion is so small that it's only noticeable for every one part in 10^28.
There's another model of subatomic physics that says the distortion should be much more noticeable, anywhere between one part in 10^14 and 10^19. This is the model that incorporates supersymmetry, which posits that all the elementary particles we know have a superpartner that is considerably more massive and differs by half a spin. For more on these sparticles, you can check out our primer on undiscovered particles here.