Click on image for diagrams!
This is the model I use for the Paper Review Project. You can read reviews for Elephant Hide, Tant, Japanese Foil, and Printer Paper.
To diagram and teach a tessellation I choose the Way of the Molecule. By teaching only one, it is simple to understand, diagram and fold. Next step is to try a 2X2 model, and either jump from there to what ever size you want, or to incrementally go through the 3X3 stage, which is the first to have an all-around- molecule, i.e. without any original edge of the paper. If you can do that, you can fold any number of molecules.
Like with many other molecules, one can decide if the pattern will cover all the paper, or to leave a rim around it. This model is easier to fold if left with a rim, and that is what I teach here. I have also provided a crease pattern for the two options. It is much easier to print, and fold, but it is not a must. Usually a tessellation is made in three steps: Grid; Pre creases; Collapse. This tessellation needs an extra step – the collapse is done in two separate steps. Enjoy!