Help with a celtic knot!

Hi there! First time poster.  I'm still quite new to Illustrator, but I need some urgent help.  I'm doing a celtic knot for my design job, and I need to outline the individual shapes - basically, I need to get the transparent breaks in between (i.e., like any old, traditional celtic knot design).  I've tried tracing with the curvature tool, nothing works that looks decent.  I've tried copying, pasting, inverting path and fill, it's interesting, but the way I've built it, it's completely wrong.  I basically built one half, and copied and mirrored it.   I've searched and searched, and I have NO idea how to do this, and I need to get it done relatively quickly. 

Thanks for your time in advance!