Epicycloid (0<t<90)
r=5
k=4

x=r*(k+1)*cos(t)-r*cos((k+1)*t)
y=r*(k+1)*sin(t)-r*sin((k+1)*t)
z=0

Hypocycloid (-90<t<0)
r=5
k=4

x=r*(k-1)*cos(t)+r*cos((k-1)*t)
y=r*(k-1)*sin(t)-r*sin((k-1)*t)
z=0