P Strips

Author : Gavin Theobald

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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:

Triangle strip

The square does not require dissection to form a strip:

Square strip

The best P strip for a pentagon is the following:

Pentagon strip

Here are two different hexagon strips. As will be seen later, there are infinitely many variations:

Hexagon strip Hexagon strip

A variety of heptagon strips can be found but this one is by far the most useful:

Heptagon strip

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.

Octagon strip Octagon strip

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.

Enneagon strip Enneagon strip Enneagon strip

There are a large variety of decagon strips:

Decagon strip Decagon strip Decagon strip Decagon strip

Again a variety of dodecagon strips are possible:

Dodecagon strip Dodecagon strip Dodecagon strip Dodecagon strip

Useful pentagram strips are hard to find.

Pentagram strip Pentagram strip Pentagram strip

The following is the only practical hexagram strip:

Hexagram strip

Again there is only one practical octagram strip:

Octagram strip
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