Can I join the list for watching the video?
Polygonal turning is something I'd like to be able to do, but don't have a suitable machine (yet!).
I think the Polygon Machines are mostly directdrive using a shaft from the headstock, however quite a few CNC lathes with live tooling are capable of it using software syncronisation.
It doesn't produce perfect flats, however with a suitable choice of cutter diameter, number of cutters and drive ratio (I do have a tooling catalogue somewhere that lists the recommended combinations if anybody is interested), it produces flats that are good enough for spanners/sockets, which is where polygonal turning is mainly used.
Moray