We can dissect a shape to form a tessellation. From this tessellation we can select a variety of strips:
Combining this with a hexagon strip or a dodecagon strip gives the following two dissections. For each dissection we choose the octagon strip that best fits.
This degree of freedom in the design of the octagon strip often allows us to save a piece.
The same method works when dissecting the enneagon to the hexagram or the golden rectangle.