In folding a tessellation is a shape that is repeated over and over again. It can be (more or less) flat, or tree dimensional. It can be very regular or have interesting variations.
If you want to repeat a folded shape, most of the time, you will have to do some clever problem solving. Have a look at these folded box shapes. The raw edges are sticking out in pointy flaps at the corners. It is impossible to form a tessellation. They do not fit together.
magic ball tessellation
The magic ball tessellation is also sometimes called water bomb tessellation. It forms a three-dimensional surface that is very flexible.
This crease pattern shows a simplification of this type of folding. If you fold it, you will see that the (vertical) mountain fold in the middle is pushed alternating to the left and the right, into the valleys that are formed by the pleats.
- Make a four by four-square grid.
- Subdivide in one direction so you get a four by eight grid.
- Place alternating crosses.
- Pre-creased the vertical lines in mountain folds, the horizontal creases in both directions, and the crosses in valley folds. Use an empty pen and a ruler to score the crosses on the paper before you fold the creases.
There is more than one way to collapse the paper. Have a look at the following tutorials to decide which one will work for you.
In some tutorials, the diagonal creases are folded all the way from one side of the paper to the other. Do not do this, it will make the final folding of the object much more difficult than it needs to be.
This folding is very suitable for experimentation. You can pop pyramids shapes in the other direction, change proportions in the crease pattern, form squares, and make one small valley out of two adjacent waterbomb shapes.
If a folded object is very irregular, it can be placed between two heavy objects with a plate over it.
This Tessellation was made by changing angles and dimensions in the crease pattern.
The categories I make for different types of Tessellations on this site are mostly arbitrary. They exist to organize the site you should not put too much value into them.