Square Twist

The above images show the simplest square twist pattern - one unit, four units, 16 units, and 64 units sucesisvely. Each is folded from a single sheet of paper.

The square twist is one of the simplest kind of unit for a tessellation. Here are instructions for folding one unit:

There are lots of different ways of putting square twists together to make a repeating pattern.

Eg, put four together like this:

It's easiest if you do precreasing first, that is, put the following creases into the paper before you begin to twist the squares:

If you want, you can just put the following creases in:

(ignore the dotted lines). In the second case, you need to fold everything "all at once". In the first case, you can fold bit by bit; you need to remember which squares are to be twisted.

With many tessellations, you need to fold all the folds gradually at the same time. This is not necessary for the square twist pattern, but the precreasing helps a lot.

The above images are of tessellation patterns obtained in very simple ways from the simplest square twist pattern, just by adding extra folds in various places after folding the basic pattern as above. The last image shows a set of 9, all displayed together, between plexi glass.

You can put the squares closer or further apart, and make different sized twists in the same piece of paper. All kinds of things.

Or even do one on top of the other. As long as you are careful with the folding, you can produce a nice ziggurat without a lot of precreasing, like this:

Ziggurat

1. Make the following creases. It doesn't matter too much how far apart the parallel lines are, but the closer together, the more levels your ziggurat can have.	2. Twist the square, as in the above instructions, except diagonally on to get this:	3. Now make the following creases on top of what you've got:
4. And twist again:	5. You can keep on doing the same thing over and over, to get lots of squares on top of each other:	6. When you've got at least two or three twists done, pull the top square upwards, and open out the levels to get the ziggurat:

If you just want one, you can fold over the corners of the paper and tuck them neatly together underneath.

Or if you start with big enough paper, it's possible to tessellate these to make a field of ziggurats, i.e., many all in the same sheet of paper.

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