The involute of the astroid is a hypocycloid involute for . Surprisingly, it is another astroid scaled by a factor and rotated of a turn. For an astroid with parametric equations
(1)
 
(2)

(3)
 
(4)

The involute of the astroid is a hypocycloid involute for . Surprisingly, it is another astroid scaled by a factor and rotated of a turn. For an astroid with parametric equations
(1)
 
(2)

(3)
 
(4)

Weisstein, Eric W. "Astroid Involute." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/AstroidInvolute.html