# Origami Tessellations

Before you read about origami tessellations, do you know what is a tessellation? If not, please read this section first.

Origami tessellations have visual similarities to the tessellations mentioned above; but they are physically quite different. An origami tessellation is not made of separate pieces of paper placed side by side: instead, they are made with one sheet of paper. This one sheet of paper is folded such that it has a tessellated pattern. [Photo by Andy Wilson]

Origami tessellation may have been started by Shuzo Fujimoto in the late 1960's. He self-published a few books with origami tessellation examples in them and in 1976, Fujimoto's "Solid Origami" was the first commercially published book containing origami tessellaions. Artists including Chris Palmer, Tom Hull, Helena Verrill, and others have developed the art form further. Today, you can see a wide selection of origami tessellations in many Flickr photo sites. More information about the history of origami tessellations can be found in David Listers' essays on Paper Tessellations and their Diagrams.

Method 1: Unlike traditional origami, origami tessellations are not made in a linear step-by-step fashion. There are very few instructions on how to fold an origami tessellation and the way you fold is a matter of personal preference. One method is to:
• Drawn or print a crease pattern onto a piece of paper.
• Crease the paper with mountain and valley folds.
• fold the pre-creased paper into the final shape.
• [Image: origami tessellation crease pattern from A Bateman (see finished tessellation here]

Method 2: Another method is to fold an entire sheet of paper into a a grid and then create a model from this grid of creases. When folding the pre-creased paper into the final model, it sometimes works best to start from the center of the paper and work outwards. Alternatively, begin working from one edge of the paper and extend towards the opposite edge. Often, the pre-creased paper needs to be jiggled and tugged to coerce it into its final shape. Three words of advice: patience, practice, and perseverance.
• Read about Rikki Donachie’s first tessellation which took 3 hours of creasing and over 4 hours of paper-coercion.
• Eric Gjerde's web site has many crease patterns.
• Helena Verrill's gallery has some crease patterns.
• Alex Bateman's flickr site has crease patterns.

Most origami tessellation models are flat. They have no volume and look like a piece of paper with geometric designs on it. A closer examination of the model will show that it is not uniformly flat – there are raised ridges where multiple layers of paper lie one on top of another.

If you hold the model up against a light source, the amount of light passing through the sheet of paper will depend on the number of paper layers. Often, you can see a pattern that is more elaborate than the one seen from a surface-view of the model. [Photo: Flor by Melisande]

Some origami tessellations pop-out above the plane of the paper. These models have depth and can be considered 3-dimensional. [Photo: hexagonal tessllation stars, top and bottom view. By Melisande]

Don't be fooled though, some models appear to be 3-dimensional but are actually flat models. This is seen in Eric Gjerde's Spread Hex Tessellation. Here, hexagons are stacked so that the model has height due to the thickness of the paper but, it is actually a flat model. [Photo: E Gjerde's Spread Hex Tessellation].

Fujimoto's pyramid is also a flat model, but Joel Cooper used paper that was flexible enough that he could "stretch out" the model to appear 3 dimensional. A more traditional rendition of the same model is squished flat. [Photo: variation of Fujimoto's pyramid folded by J Cooper]

 Lastly, some models are not strictly origami tessellations, but have tessellations incorporate within their design. Particularly noteworthy are Joel Cooper's masks. These are made with a method called "pleating" but they also contain large sections of tessellated origami. Robert Lang's Koi fish has tessellated sections to simulate fish scales. [Photo: Mask by J Cooper and Koi fish by R Lang]

You can Tessellate Too