To go forward with the similiar Mandelbrot Set and Phi in the shape of the Golden Spiral being heart shape we now have to examine an Envelope Cardioid which has to have the right amount of envolopes to cut through the inner circle, we need ten 36 degrees apart, although if you click on link you will find the circle on the inside unlike the the mandelbrot set image below, please scroll down link:-
[mathworld.wolfram.com]

[en.wikipedia.org]

So the golden spiral joined to mirror image produces approx. the same cardioid. A bigger image to the above link is below:-

[files.abovetopsecret.com]

How to draw a pentagon is below:-

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We can now join both shapes together that fit like a glove shown below:-

[files.abovetopsecret.com]