Each time I think I've got a perfect shape to throw at the Network tool, I'm quickly humbled. I don't think I've ever truly gotten the hang of this tool. I'm attaching a group of curves that I'd like to network, but I'm having no luck. Is there any way to network this frame? My questions about this command always seem to be along the lines of:

How many curves do I need? Do I have too many, too few?
Should my perimeter curves be closed or segmented?
Should be internal curves be lying on top of each other or segmented where they meet?

I've tried multiple approaches on this shape, but I get a calculation failure each and every time.