A tessellation is a symmetrical design where the pieces fit together like a jigsaw puzzle with no gaps or overlaps. An origami tessellation uses pleats to connect modules together in a repeating fashion. The design is made from one large sheet of paper.
Classic origami tessellations always have an odd number of layers and produce interesting effects when the model is backlit. One layer will be slightly transparent, while the others will be progressively darker.
Shuzo Fujimoto is thought to have been the first person to seriously study origami tessellations. Robert J. Lang has used computer programs to help aid in the creation of origami tessellations.
Other noted artists who often complete origami tessellations include Eric Gjerde, Joel Cooper, Christine Edison, Ray Schamp, Chris Palmer, Polly Verity, Tom Hull, Alex Bateman, Roberto Gretter, Goran Konjevod, and Christiane Bettens.
The principles used to make origami tessellations are based in geometry, so it's not surprising that many people who study origami tessellations have a background in mathematics. Shuzo Fujimoto was a mathematics teacher. Robert Lang is a physicist who has extensively studied the mathematics of origami. Alex Bateman and Tom Hull are both mathematicians.
The word tessellation originates from the Latin tessera, which means “a small block of stone, tile, glass, or other material used in the construction of a mosaic.” The honeycomb is an example of a tessellation in nature.
Supplies for Making Origami Tessellations
Elephant Hide or Tant are the most popular types of paper used to make origami tessellations. Glassine paper is good for using when you want to highlight the transparency of the various folded layers in the tessellation.
Clips are useful for holding pleats in place as you're working. Generally, you use use two clips per pleat. Extra bits of paper can be inserted into the clipped area to prevent the clip from leaving a mark.
A bone folder helps make it easier to create sharp creases. Bone folders are also used by card makers and are widely available at any major craft store.
Blu-Tack, a reusable putty-like pressure-sensitive adhesive, can be used to make guide marks on the paper as you're working in order to keep you from becoming disoriented.
Origami Tessellation Tips
The process of folding a tessellation can be broken down into three parts: grid, precrease, and collapse. One general technique that is quite popular is to draw or print the crease pattern on your paper before adding the appropriate mountain and valley folds. Then, you can gently coax the precreased paper into the final shape.
Tessellations are usually made from grids that are created by dividing the paper into equal parts in both directions. A 16 x 16 grid is good for the beginner. Most advanced folders may want to tackle 32 x 32 or 64 x 64 grids.
Square grids are easiest for the beginner. Hexagon, triangle, rectangle, or diamond grids should be attempted once you can successfully make a square origami tessellation.
Tessellations are mostly based on precreases, so this type of origami requires a great deal of patience and persistence. The larger the grid, the more precreases will be needed.
When collapsing a model, work from center to edge or collapse the creases row by row from the corner.
Origami Tessellation Examples and Instructions
If you would like to see a video demonstration of someone making origami tessellation, there are several excellent tutorials on the Happy Folding by Sara Adams YouTube channel.
There is an impressive Flickr group of over 8,000 different photos of origami tessellations posted by artists from around the world.