There are so many variations of the basic Byzantine pattern, it is hard to think of them all.
I teach a Byzantine class at my local bead store, Beadcache in Mansfield, MA (http://www.beadcache.com/) When you are teaching the basic pattern, it is hard to know how far to go with so many possibilities. Usually, I give them a choice to make a bracelet that is all Byzantine or one generally called Byzantine Rose. Well, as you might guess, Byzantine Rose wins hands down.
The Byzantine Rose pattern includes a "rose" that is simply 3 rings each inside the other. Fancy name is : Mobius ball. You make several segments of Byzantine and attach the segments with "roses" in between each segment. "Ta - Da", an interesting beautiful bracelet.
I must interject to tell you that you will see almost any Chain Maille pattern by more than one name. Byzantine, for example, is also called Bird Cage and Queen's Maille. Now back to your regularly scheduled program.
One of the favorite Byzantine variation patterns is Romanov. Personally, I think it is so popular because you can add beads - or not. This is made by making several segments of Byzantine and connecting two of them with a larger ring at the top. A bead can be added in the center. (Cobalt is always a winner too)
I'll have a few more variations for tomorrow. Until then,