ooppss!
Ignore that. :roll:
After I posted that, I was cleaning the floor and realized I wrote an answer to another question I'd been figuring out for myself. I've had hexagons and pentagons and penroses floating around in my head for days.
By the time I got back, I couldn't edit it.
The octagon info is correct - in order to make a square, you can use a HST on each of the 4 corners.
For the hexagon, you need equilateral triangles - 60 degrees at each angle, and all 3 sides the same length.
The easiest way to cut those is from a strip. But since they're the same no matter which way you orient them, you need to be careful that the straight of grain edge is always placed next to the top or bottom edge of the hexagon.
Otherwise, you've got bias on the outside edges. A lot of starch of the fabric before it's cut will help contain that.
I usually stack them together with a pin along the straight edge so I can keep track.