Origami & Folding
what one sheet can do
Generator

The property belongs to the pattern

A generator in the tessellations library, called 7 times across 3 essays. Below: what it draws with nothing specified and with the settings the essays give it, what it checked while drawing, and everywhere it is used.

metamaterial-response is one function. Everything below was drawn by it when the site was last published, at settings taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and when the generator changes, this page changes with it.

With nothing specified

The property belongs to the patternPoisson's ratio against fold state, measured off the solved motion for three Miura panels and for a plain accordion of the same paper. The accordion holds at zero for its whole travel, so this is not something folding does in general; and the Miura's value changes by an order of magnitude as it closes, which is not something a material can do.00.20.40.60.80123how far the sheet is closed−ν, so every curve shown is a negative ratioMiura, slant 0.25Miura, slant 0.42Miura, slant 0.6accordionexactly zerothe same paper,three behaviours,chosen by the creasepattern alone

slants: [0.25, 0.42, 0.6]

The property belongs to the patternPoisson's ratio against fold state, measured off the solved motion for three Miura panels and for a plain accordion of the same paper. The accordion holds at zero for its whole travel, so this is not something folding does in general; and the Miura's value changes by an order of magnitude as it closes, which is not something a material can do.00.20.40.60.80123how far the sheet is closed−ν, so every curve shown is a negative ratioMiura, slant 0.25Miura, slant 0.42Miura, slant 0.6accordionexactly zerothe same paper,three behaviours,chosen by the creasepattern alone

slants: [0.35, 0.5, 0.7853981633974483]

The property belongs to the patternPoisson's ratio against fold state, measured off the solved motion for three Miura panels and for a plain accordion of the same paper. The accordion holds at zero for its whole travel, so this is not something folding does in general; and the Miura's value changes by an order of magnitude as it closes, which is not something a material can do.00.20.40.60.80123how far the sheet is closed−ν, so every curve shown is a negative ratioMiura, slant 0.35Miura, slant 0.5Miura, slant 0.785accordionexactly zerothe same paper,three behaviours,chosen by the creasepattern alone

slants: [0.15, 0.3, 0.5, 0.7]

The property belongs to the patternPoisson's ratio against fold state, measured off the solved motion for three Miura panels and for a plain accordion of the same paper. The accordion holds at zero for its whole travel, so this is not something folding does in general; and the Miura's value changes by an order of magnitude as it closes, which is not something a material can do.00.20.40.60.80123how far the sheet is closed−ν, so every curve shown is a negative ratioMiura, slant 0.15Miura, slant 0.3Miura, slant 0.5Miura, slant 0.7accordionexactly zerothe same paper,three behaviours,chosen by the creasepattern alone

What it checked while it drew

Collected while it drew, not written by hand. The count is how many separate times that claim was put to the test.

Where it is called

Every figure listed here is drawn by the same rule, so a mistake in the rule would be in all of them at once, and so would a correction.

A material made of creases

A folded sheet has a Poisson's ratio, a stiffness and a packing behaviour that the flat sheet did not. None of them belong to the paper — they belong to the pattern, and changing the pattern changes them without changing the material at all.

A metamaterial with no edge

A folded metamaterial's properties are quoted per unit cell, because a material is supposed to be the same everywhere and a cell is supposed to stand for the whole of it. Every cell this collection has measured has been cut out of a patch, with a rim round it — and a rim is the one place a repeating material is not like itself.

Bought with holes

A Miura-folded sheet gets wider as it is pulled, and by how much depends on its panels and on how far it happens to be folded. A sheet cut into squares joined at their corners does the same thing and holds the value at exactly minus one, everywhere in its motion — the same property, bought with different geometry, and paid for in holes.

All the figures · The tessellations field · The patterns a reader can fold