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 just straight 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 to the second one:
A variety of heptagon strips can be found but this one is by far the most useful:
Here are four octagon strips. Note that though the second one requires more pieces, 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. The first two strips below can be varied in many different ways. 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. It is possible to make strips from only three pieces, but such strips do not appear to be very useful.
The following is the only practical hexagram strip:
There are no simple and useful {8/2} octagram strips although we will look at how to create such strips on a later page.
There is only one practical {8/3} octagram strip:
Here are a couple of {10/2} decagram strips. It would be better to have strips with fewer pieces.
Here are some greek cross strips:
Finally, here is the latin cross strip: