When , the superellipse looks like a four-armed star with concave sides. In particular, when 2/3 and , 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 , the superellipse is a diamond with corners and .
When , the superellipse looks like a rectangle with rounded corners. In particular, when and , the figure is called a "squircle" because it has properties between those of a square and those of a circle.