Deltoid

The hypocycloid with three cusps, drawn by a point on the rim of a wheel turning inside a circle of three times its radius. A segment of fixed length can slide with both ends on the curve while staying tangent to it, and one round of the point of contact turns the segment end for end. This was long thought the least area in which a needle can be turned round, until Besicovitch showed in 1928 that the area can be as small as you like.

z = 2a e^(it) + a e^(-2it)

On mathcurve.com as Deltoïde