Offset not working with shape

I am trying to draw a hypocycloid and then create a banded hypocycloid within it that I can use push/pull to give it an embossed feel. The end result would be a three hypocycloid shapes, with the innermost and outermost hypocycloids being on the same plane and the “band” created in between them by the middle hypocycloid being raised or lowered.

Since there is no hypocycloid tool, I had to draw one using arcs. As a beginner, it took a lot of playing around to get it properly lined up to mirror in both directions and also have everything connected to create a face. Now that I have my four connected arcs with a face, I’m trying to use the offset tool to create the two inner hypocycloids, but it won’t grab the edges or manipulate my shape.

I tried using copy/paste and then resizing the copies, but this changes the curve of each arc so they don’t maintain a consistent distances between inner and outer hypocycloids. I feel like offset should be the tool that would get it right. Any suggestions? I’ll attach the file.

Diamond Inset.skp (108.3 KB)

Here is a modified version to show the effect I’m going for using a simple circle shape that was changed using the offset tool.Diamond Inset.skp (148.9 KB)

I would start this way…

Brilliant! Thank you! I’m completely new not only to 3D graphics, but to graphics in general. You’re never too old to start a new hobby!