Origami & Folding
what one sheet can do
Concept

Found pattern — where it appears

A crease pattern that a structure falls into by itself, under load or growth, rather than one a designer drew. Crushed cylinders find the Yoshimura's diamonds and twisted ones the Kresling's slanted triangles; that buckling chose them is why they satisfy the folding conditions, and also why their proportions are not free.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

found rather than designedcrushed drink cans, tree bark,deployable boomsat every interior vertexsectors 60°, 60°, 60°, 60°, 60°, 60°two courses and four diagonalstwo of one letter, four of the otherwhy the height is not freea steeper diagonal makes the topsector strictly smallest, flankedby two of the same letter20 interior vertices · 23 mountain and 56 valley creasesmountainvalleyraw edge

Patterns nobody designed

Crush a thin cylinder and it folds into a diamond lattice. Nobody chose the pattern — it is the buckling mode with the lowest energy, and it satisfies the flat-folding theorems because it just folded.

tessellation · Found patterns one strip of triangles, two tubes2 courses of a 6-sided Kresling tube, both diagonals at their own length in eachas made: 1.79 a course, turned 80°second state: 0.99 a course, turned 160°long diagonal 2.204, short 1.824long diagonal 2.204, short 1.824

A twisted tube has two heights

Twist a thin cylinder and it falls into a pattern of slanted triangles that clicks between two lengths. The click is usually explained as a fold, but there is no fold. Every crease keeps its own length at exactly two heights, and in between both diagonals have to stretch or shrink. The second height exists only on a course made taller than the one that folds flat, and the Yoshimura's course, the same pattern with no lean, has its second height on the far side of the tube's own axis.

tessellation · Found patterns four courses holding the word 1010each course clicked shut or left open, read from the bottom upA: made 1.30 H, shut, 1.24 tallB: made 1.45 H, open, 2.16 tallC: made 1.60 H, shut, 1.86 tallD: made 1.75 H, open, 2.61 tall

Four clicks make sixteen lengths

A Kresling tube of four courses has sixteen ways to be at rest, each course shut or open. Pressing and pulling it under one force can reach all sixteen or only five, and the difference is set by how tall the courses were made. Every course shuts at a force that falls as it is made taller, while the force that opens it rises to a peak and then falls. A stack graded below that peak opens shortest first and can only count. Graded above it, it opens tallest first and can be written like a register.

tessellation · Found patterns

Named alongside it

The objects these essays reach for when they reach for this one.

Energy minimisationThe Yoshimura patternBucklingCylinderCrumplingRigid foldingSymmetry breaking

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