This Reuters video (and I'm sorry about the 30 second commercial that you have to sit through to get to it) depicts "Britain's Most Natural Beauty," where the contest "wasn't just a matter of subjective beauty, but settled with science. Researchers said that the distance between facial features, and the width and length of the face are deciding factors for perfection." Some of the text from the video can be read here, though you'll miss the depressing images of her working in a fish 'n chips shop.
This follows the ancient Greek tendency to equate beauty with harmony, which would make it objective and mathematical. Our modern pluralism argues against that, of course, and I see a parallel in our deliberations about the relativism of humor. As I said on the episode, different kinds of humor are trying to do different kinds of things. Not all of them are at even supposed to be laugh-inducing, and we laugh for multiple reasons, not all of which are even related to something we'd for sure call humor. But given a particular standard, there may well be a logic to it that can be measured, so you can objectively tell if someone's singing in tune, or whether the colors in a painting our outfit are harmonized, or in this case, you can measure the mathematics of the face. Clearly, though, such an exercise doesn't rule out questioning the standard itself by asking whether meeting that standard is necessary or sufficient for beauty or humor. Something that comes close to some fairly natural (or historically rooted, at least) standard could turn out to, on reflection, be not at all what we find most important in art/humor.
We've been long planning an aesthetics episode on George Santayana's The Sense Of Beauty,and he describes the different layers/aspects by which we take in an object of aesthetic contemplation, e.g. the surface play of colors in a painting vs. the shapes which may have their own appeal vs. the intellectual relations between the ideas conveyed vs. the associations that we may bring to any of the preceding vs. external factors like knowing who the artist was or how much it cost. Without getting into the specifics of that theory, we can see that one can, like Santayana, try to explain the multiplicity of standards by focusing on the different aspects of the work, such that people who disagree on whether something is beautiful are just paying attention to different things (or bringing different things to it), and this retains the character of a theoretical explanation, a schema for explaining beauty, as opposed to the irreducible relativism that says that "we just like different things" and admits of no further explanation. I'm not prepared yet to come down on one side or the other here, but it's a question I'd like to follow further.