I read Your Inner Fish and got inspired for a new creature:)
So we humans are bilaterally symmetrical, with a functional difference between front and back, and another between back and belly. But there’s no functional difference between left and right. In the same way, jellyfish have a difference between up and down, but no front versus back.
What if we had an animal with three axes of asymmetry? Right vrs. left is as different as back-vrs.-front and top-vrs-bottom. But while it’s easy to see why a worm crawling along the ocean floor would evolve a head and a belly, why would it evolve a specialized structure on its right as opposed to its left side? What force could there be that always acts on an animal orthogonally to gravity and its direction of motion?
UPDATE:
Similar to Julio Nicoletti ‘s idea of tri-axiality evolving on a world tidally locked to its sun, what about a moon tidally locked to a gas giant? Would the gas giant have some effect on the ground that lifeforms might adapt to?
Or what about a planet with a very strong magnetic field? Then the North side of an animal would have to be different from the south.
Another idea: a cold planet where geothermal heat is the primary source of energy so hot-cold becomes an axis of symmetry.