Cardioid Involute

$\begin{figure}\begin{center}\BoxedEPSF{CardioidInvolute.epsf scaled 700}\end{center}\end{figure}$

$\displaystyle x$	$\textstyle =$	$\displaystyle 2a+3a\cos\theta(1-\cos\theta)$
$\displaystyle y$	$\textstyle =$	$\displaystyle 3a\sin\theta(1-\cos\theta).$

This is a mirror-image Cardioid with