The first stage to finding most dissections is to first dissect each shape and then to rearrange the pieces to form a strip element. By putting these strip elements end to end a P strip is formed. The "P" here stands for Parallelogram as this is the shape of the strip element. In reality the strip element is frequently not a simple parallelogram as the ends of the element are not normally simple lines.
The best strips require the fewest pieces, but this is not the only consideration. It is also useful to have strips where the largest piece is as large as possible.
The following is a strip formed from an equilateral triangle:
The square does not require dissection to form a strip:
The best P strip for a pentagon is the following:
Here are two different hexagon strips. As will be seen later, there are infinitely many variations:
A variety of heptagon strips can be found but this one is by far the most useful:
Here are a couple of octagon strips. Note that though the first one requires an extra piece, it is still very useful because of the large size of the largest piece. Many other strips can easily be found.
A large number of enneagon strips are possible. Unlike the heptagon, there is no one strip that stands out as being more useful than the rest.
There are a large variety of decagon strips:
Again a variety of dodecagon strips are possible:
Useful pentagram strips are hard to find.
The following is the only practical hexagram strip:
Again there is only one practical octagram strip: