Omelets vs. Frittatas
The most important difference between omelets and frittatas is that omelets are fried on only one side whereas frittatas can be fried on two sides. As a fan of the Maillard process, I think the more surfaces fried the better.
I'm starting research into the topological investigations needed to produce a three-sided frittata. (ObSF: “No-Sided Professor” by Martin Gardner)