Be careful. While a proof in Lean is executable (it is a script, so to speak) it is conceptually a sequence of references to tactics. Writing a Lean proof does involve a highly specialised form of functional programming, but I wouldn't be at all sure that becoming an expert in Lean would improve your programming skills across the board.
Your comment also reminds me of the people who claim that the Curry-Howard isomorphism means "programming is math". It's not a claim that anyone should really be making in good faith. There's a lot more to programming than the lambda calculus.
I don't know exactly what you mean, but the name of this shape is consistent with the naming of traditional geometric constructions like the "five-centered arch" and the "three-centered arch" (see many diagrams online for details of these constructions).
So "four-centered egg" might make more sense to you, though it could also be called the "six-centered egg", because it includes both sides, unlike the classical arch constructions.
Your comment also reminds me of the people who claim that the Curry-Howard isomorphism means "programming is math". It's not a claim that anyone should really be making in good faith. There's a lot more to programming than the lambda calculus.