Pulling out central vertices of polygon

On a festive theme, I’m trying to produce a printing pattern for a 3D ‘star lamp’, something akin to this:

I’m afraid that, try as I might, I can’t seem to find a solution to pulling out the centre of the star along with the cutouts (in orange on my model). The individual faces are easy enough to create, by splitting the star into 7 segments and using the central control point to pull out the centre, then splitting the deformed curve with a line. However, how I go about pulling the cutouts forward too, I really can’t work out.

I’m treating this as a bit of a learning exercise for Rhino, I hope someone on the forum may be able to help?

Some quick screengrabs of where I’m at:

There are several ways to apply curves to a surface. In this case, I think that project will work best.

maybe try using RailRevolve

the setup would look something like so:
(green curve = profile curve… star is the rail curve… the vertical white line signifies the revolve axis)

resulting in: