Variable Strips

Author : Gavin Theobald

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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:

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:

Decagon strip

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

Decagon strip

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:

Octagram strip Octagram strip

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.

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