If you have a dividing head, use that.
If not I'd suggest do it in the lathe the following way..
Grab a toolpost holder for your lathe and take the tool out, or use a non q/release post with no tool in it.
Set it up so that is square with the compound slide..
Using a set square or some item that will give you a center across each end diameter to work form, and divide the end diameters to the desired amounts, equally so that you can then mark out the divisions down the length of the piece.
G-clamp (or whatever) the piece in/against the tool post or holder and set the compound slide to the angle you want, put some class of endmill in your chuck and mill out the flats using the cross slide.
Do the taper afterwards because you left enough material to chuck it up after the flats get done, however you might need to do the taper first, and set your toolholder to the required offset...
Use the marks you put down the length of the work to line up with some reference point on the toolpost to get equality (lol), so you can turn it to the next section more easily.
Experiment with some other piece of scrap till perfected, till you get the method down pat, and go.
Make more than one, sell the rest on fleabay or some where........
Just my 2 cents.......
BTW 10 thou is 1/4 mm, try to achieve the best tolerances you can, because with facets they need to be quite equal in size and spacing or you can see the sloppyness really easily
because each facet visually acts as a refrence point in the minds eye for the next facet to it......so 10 thou will look like you filed it out with blunt woodaxe., probably.........and if you are 10 thou out one side that is 20 thou of/on the facet next to it, most likely. so bear that in mind also.......good luck....