|x/a|ⁿ + |y/b|ⁿ = 1 — the family between diamonds and rectangles
A superellipse (Lamé curve) is defined by |x/a|ⁿ + |y/b|ⁿ = 1. When n<1 it forms a star-like astroid; n=1 gives a rhombus; n=2 an ellipse; n→∞ approaches a rectangle. Piet Hein popularized the "squircle" (n≈2.5) for urban design — the shape is neither ellipse nor rectangle but something naturally comfortable. Gabriel Lamé studied these curves in the 1800s.