Hhm....there may be a few different ways to approach it. My first thought is to try using Live Path Effect > Envelope Deformation. I can't remember if it can be applied to a group though. If it can't, then there's also an Envelope Deform extension. One of them can be applied to a group, I just can't remember at the moment, which one. However, I don't think you could achieve this result with the extension.
Another way might be with Interpolate extension (Extensions menu > Generate from Path > Interpolate. In this scenario, you would not start with a rectangle and lines. You would start with the line that forms the top of the rectangle, and the line that forms the bottom of the rectangle, and they would already have to be curved in the proper manner. Perform the interpolation on those 2 lines to create the 4 in between. After that you would draw new lines to conntect the top and bottom lines (Pen tool), and use the Node tool to make the curves.
And there may yet be other ways to do it, and I'm sure other will reply with more tips. It's an interesting task
This is a read-only archive of the inkscapeforum.com site. You can search for info here or post new questions and comments at 
