Plane Curves as Mobiles

Here are some plane curves, hypocycloids, made three dimensional by extending them along the z axis as was done for the epicycloids in thing:217201 - Epicycloids as Mobils.

Hypocycloids and epicycloids are closely related; a single sign change in the parametric equations for an epicycloid changes it to a hypocycloid. Like the epicycloid the hypocycloid can have multiple cusps; 3 cusps is a deltoid, 4 cusps is an astroid, 5, 6, 7, etc. cusps are possible and a circle occurs when the number