Surely the meaning of "faith" is straightforward enough: Belief without evidence.

Yes, but not exactly. First, symmetry is a property of an object, whereas beauty isn’t. You can consider an object beautiful one day and not beautiful the next even though it hasn’t changed. Rather, if a creature observes something, “beauty” seems to be a perception the creature has about his perception of the object. But even though it's second-order or whatever the correct terminology is, yes, I am talking about beauty as a “real” thing. I don’t know much about neuroscience, but I suppose you could conceivably observe “beauty” with an MRI (?), trained to recognize the signature of that experience.

To the extent which beauty is a real thing, that’s science. What science doesn’t give us is that the experience of beauty is significant in and of itself. By significant ‘in and of itself’ I mean that it’s not just significant because it is useful in helping us select a healthy mate, but in some way inherently awesome. I'll use awesome here as possessing some significance additional to the significance that can be scientifically demonstrated. Of course the perception of awe could be recognized by the MRI. Theists describe this as feeling that the uinverse is purposeful and connected, but I will give a non-magical definition. If beauty is an inherently awesome thing, my thesis is that this awesomeness stems from its pattern in the natural world. Or rather, that the experience of awe comes from the perception of significant pattern but I'm afraid I'm being too meta already.

The following won't make sense unless you actually consider beauty some type of real thing. Beauty has resulted from the natural laws of the universe: these laws resulted in atoms, that resulted in molecules, that resulted in life, that resulted in sapient humans that resulted in the experience of beauty, observed by an MRI when a person observes something they consider beautiful. Consider the relationship of the real existing thing “beauty” with the laws of the universe – it’s analogous to some kind of mathematical structure because the laws of the universe are analogous to mathematical structures/equations. It's like some kind of sub-manifold in the phase space. This is what I’m calling “pattern”. Problematically, for us, everything that exists, including random noise, is a pattern and whether a pattern is awesome or not is interpretative, so it’s not verifiable of falsifiable. Nevertheless, humans are very good at identifying whether a pattern is awesome or not. Perhaps someone else could say more, but I just call this awesome-perception an aspect of “intuition” and know it must be contained within “good epistemology” because its what scientists and mathematicians use.

Finally, lets suppose that upon inspection, the pattern “Beauty” turns out to be just one of an infinite number of ways of solving the problem “P=motivate a creature to choose the healthiest mate”. I would then consider “beauty” real but arbitrary. On the other hand, suppose that “beauty” is a pattern that self-organizes in an infinite number of different contexts. Maybe, for example, it is present even among sapient creatures that are so unlike us they have no concept of evolution. Creating mammals and creating human minds was just one way that the universe was able to create the pattern “beauty”. And, therefore, “wow” – beauty is awesome. But this is just an illustrative example, I don’t claim to spell out what makes one pattern arbitrary and another pattern meaningful. My preference would be that significance doesn't come from the prevalence or persistence of the pattern, but in the properties of the solutions, things like critical points, asymptotes, etc. I don't care whether beauty is such a pattern, but I'd be very surprised though if "perception of truth" wasn't such a pattern among sapient creatures.