A type of chainmail weave that makes a chain as opposed to "cloth". Birdcage involves connecting single units of boxchain together with one or two rings so that the boxes alternate which way they face. It is more open and knits a little faster than boxchain. I've also heard this called byzantine.
This can actually be described in text:
1. Close an anchor ring.
2. Put two rings on it.
3. Put two rings on those two.
4. Put two rings on the previous two.
5. Grab the two rings in step 4, split them apart from each other, and fold them almost 180 degrees back so they flank the rings in step 3. Now split the ends of the rings in step three apart slightly (they will split perpendicular to the way the step 4 rings split), to expose the other ends of the step 4 rings. Close two rings through these back ends of the step 4 rings, so that the step 4 and 3 rings make a section of boxchain.
Add two more sets of two rings, split and fold the top pair, split the pair right underneath it, and add two more rings. So the pattern is three sets of two, split-fold, split, three sets of two, split-fold-split. Have fun.