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Cayley’s sextic
Colin Maclaurin, 1718; Arthur Cayley, 1867
Drop a perpendicular from the cusp of a cardioid to each of its tangents, and the feet trace Cayley’s sextic. Maclaurin first discussed it in 1718; Cayley studied it in detail, and Raymond Clare Archibald named it after him. It is the sinusoidal spiral with n = 1/3, and it crosses itself once, on its axis.
r = 4a cos³(θ/3)
On mathcurve.com as Sextique de Cayley