The Cross Lattice Tessellation, designed and folded by Joseph Baek. A printable PDF of the crease pattern is available here. Diagrams for folding one square are here: Single molecule PDF.

This tessellation is built from groups of four-pleat interactions that form squares. When it is folded with minimal grid lines, it produces a clean, architectural surface with subtle relief.

Paper

Thickness for this model is subjective, but what is necessary is a large sheet.

Folding a Single Molecule

Some step photos from the PDF containing detailed instructions for folding one square molecule on a 12×12 grid. See the single molecule PDF.

Practicing one set of four-pleat interactions on a 12×12 grid is recommended for your first try. Fold the grid first; then fold the pleats with mountain folds on the grid lines two spaces from the center and valley folds on the grid lines three spaces from the center, making a preliminary base shape at each intersection of a horizontal and a vertical pleat.

Once all the pleat intersections are in place, the petal folds can be added one intersection at a time. For the petal fold, lift the top layer of a pleat interaction (where four mountain folds come together) and fold the left- and right-side middle layers in towards the center before pulling the top layer as far as it can go (the ends of this fold will not be at grid intersections) and laying all the folds down flat.

Folding a Larger Grid

The same sequence can be followed for a pattern with repeats. First, fold the grid, then add the pleats and pleat intersections shaped like preliminary bases, then decorate each intersection with a petal fold.

Propagate across a row, then continue to the next row to avoid accumulated tension. If resistance builds, briefly undo nearby creases, relax the sheet, and re-collapse. After shaping, press under weight to set the surface.

To determine the structure of the full tessellation, plan for a 12×12 grid per molecule plus an allowance for the border on all four sides. You could vary the spacing of the rows of molecules by sliding them around on the full grid, moving them closer together or farther apart.