The Cayley's Sextic was first discovered by Maclaurin but studied in detail by Cayley.
The name Cayley's sextic is due to R C Archibald who attempted to classify curves in a paper published in Strasbourg in 1900.
The evolute of Cayley's Sextic is a nephroid curve.
Relationships with other curves:
It is a roulette, formed by a cardioid rolling over another cardioid with the same size.
The curve is the pedal of a cardioid.
It is the involute of the nephroid.
4(x2 + y2 - ax)3 = 27a2(x2 + y2)2
r = 4a cos3(θ/3)