We can dissect a shape to form a tessellation. From this tessellation we can select a variety of strips. Here are two examples based on a two piece tessellation of the octagon:
We can also create a range of strips:
Combining these last strips with a hexagon strip or a dodecagon strip gives the following two dissections. For each dissection we choose an octagon strip from the above range that produces the best results.
This degree of freedom in the design of the octagon strip often allows us to save a piece.
The same method allows us to select useful strips from many other tessellations.