5-fold symmetry?

[Philippe Hurbain]

Sometimes you need to break the rules. 
I would subfile and rotate, and ignore any rotation problem.

+1.
The first thing I would do is to rotate the whole flower (why this weird orientation in the Bi mesh???), isolate and subfile a petal, make the stem and flower heart using primitives, slightly enlarge the petal subpart to make sure it interpenetrate the stem/heart avoiding any gaps when rotated. Then create the flower from the heart+stem and 5 rotated petals, and use isecalc to create the intersection line between the 16-fold symmetry center and 5-fold petals.
Possibly the petal can be further subparted to halves + middle part.