Origami Tessellation Terms and Definitions

While you may already be familiar with origami terms like mountain and valley folds, sinks, squashes, swivels, and rabbit ears, tessellations have a vocabulary of their own.

Unfortunately, the vocabulary of tessellations is not standardized across all tessellation designers and each tessellation book uses different definitions - and different colors and symbols for their diagrams.

This can make it hard to learn, since everyone is saying things in different ways.

I try to stick to consistent definitions throughout my teaching, and to explain my terms in plain English - no math speak.

Here's my list of the most important terms to understand when you're starting to fold tessellations:

Grid: Pattern of evenly spaced folds that are used for referencing other folds in a tessellation

Square Grid: Grid folded in two perpendicular directions, typically on a square sheet of paper

Triangle Grid: Grid folded in three directions with 60 degree angles at each intersection, native to hexagonal paper and also folded on squares and rectangles

45-Degree Grid: Square grid with either half or all diagonals added

Grid (Square/Triangle): Smallest shape outlined by grid lines on a finished grid

Grid Spacing: The distance of one grid line between two neighboring grid lines in another grid direction

Single Diagonal 45-degree Grid: Square grid with one diagonal added through each grid square, forming a checkerboard pattern of alignment

Double Diagonal 45-degree Grid: Square grid with both diagonals added in every grid square

Mountain fold: Fold that forms a ridge on the side of the paper facing you - shown with red solid lines

Valley fold: Fold that forms a trough on the side of the paper facing you - shown with blue dashed lines

Pleat: A pair of parallel mountain and valley folds

Pleat Depth: The number of grid spacings apart that the mountain and valley folds of a pleat are located, typically one spacing

Tube Pleat: A pair of two parallel, mirrored pleats with two grid spacings between the closest folds of the two pleats

Accordion Pleats: Two or more pleats in the same orientation and direction that stack on top of each other in the folded form to make an accordion/fan shape

Pleat Overlap: Two (or more) non-parallel pleats that cross each other, with one pleat completely closed when the second pleat is folded

Twist: Rotationally symmetric interaction of at least 3 pleats, with an interior shape created that is not part of the pleat folds

Pleat Intersection: Interaction of multiple pleats that is not an overlap or a twist (Note: Ben Parker's definition includes pleat overlaps and twists in the category of pleat intersections)

Crease Pattern (CP): Diagram showing where the mountain and valley folds go on the paper to fold an origami pattern; for tessellations this commonly includes a grid in addition to the folds

Tiling: An abstraction of the structure of tessellations where each twist or pleat intersection gets its own box; used to categorize and design tessellations and study their symmetries

Tessellation: Repeating 2-dimensional pattern

Origami Tessellation: Repeating pattern folded from a single sheet of paper

Whew - I think that covers just about everything!

If you'd like to learn more about each of these terms, check out my Tessellation Foundations series where I show how each of these terms are put into practice while teaching the fundamental skills needed to start folding tessellations.