How to parameterize a helical tube with a "sine wave around a circle" cross section?

Question

Consider a helical tube with a circular cross section. I already can make a regular helical tube:

what's the equation of helix surface?

Now, instead of a circular cross section, I want to make it have a cross section that is a sine wave imposed over a circle, so that the resulting cross section resembles a flower:

Equation of sine wave around a circle

My two questions are:

1. How can I parameterize a helical tube that has such a cross section?
2. Is there a name for this surface?

Thank you very much!