![]() Taking all of these options into account, we have 2*4*4=32 options for arranging hexagon and triangle twists in this extended symmetry and we haven't even talked about spacing yet. Instead of just having one choice for the next hexagon out from the middle, we actually get four hexagons to choose from - closed or open on either the front or the back.Īnd that's after we choose the central hexagon (2 choices) and the triangle twist (also 4 choices)! 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.So, it turns out that we have more choices available to us than we might suspect with Hexagon and Triangle 6-fold tilings! Whew - I think that covers just about everything! Origami Tessellation: Repeating pattern folded from a single sheet of paper Tessellation: Repeating 2-dimensional pattern 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 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)Ĭrease 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 Twist: Rotationally symmetric interaction of at least 3 pleats, with an interior shape created that is not part of the pleat folds Pleat Overlap: Two (or more) non-parallel pleats that cross each other, with one pleat completely closed when the second pleat is folded Tube Pleat: A pair of two parallel, mirrored pleats with two grid spacings between the closest folds of the two pleatsĪccordion 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 Depth: The number of grid spacings apart that the mountain and valley folds of a pleat are located, typically one spacing Pleat: A pair of parallel mountain and valley folds ![]() Valley fold: Fold that forms a trough on the side of the paper facing you - shown with blue dashed lines Mountain fold: Fold that forms a ridge on the side of the paper facing you - shown with red solid lines Single Diagonal 45-degree Grid: Square grid with one diagonal added through each grid square, forming a checkerboard pattern of alignmentĭouble Diagonal 45-degree Grid: Square grid with both diagonals added in every grid square ![]() Grid Spacing: The distance of one grid line between two neighboring grid lines in another grid direction Grid (Square/Triangle): Smallest shape outlined by grid lines on a finished grid Triangle Grid: Grid folded in three directions with 60 degree angles at each intersection, native to hexagonal paper and also folded on squares and rectanglesĤ5-Degree Grid: Square grid with either half or all diagonals added Square Grid: Grid folded in two perpendicular directions, typically on a square sheet of paper Grid : Pattern of evenly spaced folds that are used for referencing other folds in a tessellation Here's my list of the most important terms to understand when you're starting to fold tessellations: I try to stick to consistent definitions throughout my teaching, and to explain my terms in plain English - no math speak. This can make it hard to learn, since everyone is saying things in different ways. 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. ![]() 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.
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