When $0 \le n \le 1$, the superellipse looks like a four-armed star with concave sides. In particular, when $n \=$2/3 and $a \= b$, the figure is called an "astroid" because it is a hypocycloid with four cusps. [To learn more about hypocycloids, see the "Epicycloid and Hypocycloid" Math App.]

When $n \= 1$, the superellipse is a diamond with corners $\left(\pm a\, 0\right)$ and $\left(0\,\pm b\right)$.

When $n \> 2$, the superellipse looks like a rectangle with rounded corners. In particular, when $n \= 4$ and $a \=b$, the figure is called a "squircle" because it has properties between those of a square and those of a circle.