All these different names are very interesting:
Here are some templates for making a "Periwinkle Star" - but I think that would be only for hand piecing.
Or EPP (cutting off the seam allowances).
I wouldn't bother attempting this by machine - doable, but I'm not a masochist.
http://www.ozquilts.com.au/periwinkle-star-p17031.html
And here's the piecing for the Arkansas Star (as a 9patch) - this looks to have the easiest piecing and would still get you the octagon, but you do have those extra seam lines.
http://www.pieceandquilt.com/2011/07...r-month-6.html