# Variable Strips

### Author : Gavin Theobald

With variable strips we form a strip that is not fixed in the way that it is
formed. Our first example is an octagon strip:

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 following decagon strip is the basis for our next example:

What is clever about this strip is that we have lots of freedon to modify the shapes
of some of the pieces, for example:

Combining the first decagon strip with a strip of squares gives the following
8 piece dissection:

But by modifying the decagon strip we can save a piece as shown below:

As can be seen this technique can lead to some odd shape pieces.

Below we show two more examples. The first
is a dissection of the decagon and dodecagon. The second is a dissection
of octagon and decagon that also makes use of the variable octagon strip
demonstrated above. In both examples we show first the unaltered overlay
and then the optimised overlay.

Note also that a T strip version of the above decagon strip is possible which
can also be modified. This is used to dissect the triangle
to a decagon.

A final example shows a T strip of the octagram and a modified version:

Combining with the T strip for a triangle gives the following TT2 dissection:

Similar dissections are used to dissect the
pentagram,
hexagram and the
golden rectangle to an octagram.
The last of these requires a much more extreme modification. The
latin cross uses a different octagram
strip for modification.