I am actually supposed to be typing, but I just had to post this. Loie Fuller was probably the most famous proponent of this style, but it was a popular dance throughout musichalls (which were very popular theatre-like entertainment venues for the working-class, which used a variety of performers in comedy, ventriloquism, dance, occasional general nudeness, and comic songs )
The Butterfly dance was created with a loose flowing garment with long side panels, which were stiffened with long poles, and rapidly swirled in various patterns, creating an odd vortex-like pattern.
It it almost hallucinogenic watching this- rather like looking at a fractal music visualiser- very alien and artificial but very flowing and natural at the same time. At first it just looks like the performer is wildly flinging her arms about, but as you pay more attention you realise that it actually takes a lot of good timing and requires concentration to avoid getting into a hopeless tangle.
This video has a lot of different performers, so I recommend watching the lot- the individual styles vary quite a bit, though you might start recognising some stock moves. It looks like it could be incorporated into Poi performances to good effect as it has some qualities in common!