Origami & Folding
what one sheet can do
Concept

Reproducibility — where it appears

Whether a measurement returns the same answer when it is made again, by the same method or by another. A quantity computed two ways that share no arithmetic is reproducible in the stronger sense, and the two computations disagreeing is how an error in either of them becomes visible.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

what is recorded, against what is left to the folderThe preliminary base8 panels · 15 bits of orderThe Miura fold24 panels · 79 bits of orderThe square twist9 panels · 18 bits of orderThe hexagon twist13 panels · 33 bits of orderThe Yoshimura pattern65 panels · 302 bits of orderFold and cut — the triangle7 panels · 12 bits of orderThe tapered corrugation28 panels · 98 bits of orderThe waterbomb tessellation52 panels · 226 bits of orderthe pattern, as every format records itthe order of the panels, which none of them does

The file records no verdict

A crease pattern file records vertices, edges and letters. Every one of the square twist's two hundred and fifty-six admissible letterings makes a perfectly valid file, and two hundred and forty-eight of them describe an object that does not exist. The format has a field for the layer order — the one thing that would settle it — and nothing fills it in, so a file is a drawing rather than a claim, and the field exchanges them as though they were claims.

history · Notation the length a pattern reports, and the length a sheet of paper hassix of the eight are built on a unit square, so on those the distinction does not arisepatternown widthraw lengthreportedon paperThe Miura fold6.3739.36,6791,049out by 6.37xThe tapered corrugation1.187.81,2431,057out by 1.18xThe preliminary base1.004.8724724the sameThe square twist1.004.7704704the sameThe hexagon twist1.006.1916916the sameThe Yoshimura pattern1.0014.02,3802,380the sameFold and cut — the triangle1.001.7258258the sameThe waterbomb tessellation1.0014.32,2902,290the samea builder working in cells returns a pattern several units across, and not dividing by that is the whole of the error

A length needs a scale

These essays measure crease length, and a crease length is a length in the pattern's own coordinates. Six of the eight printed patterns are built on a unit square, so their coordinates are sheet widths and the distinction never arises. Two are not — a Miura laid out as six cells of unit width spans 6.37 — and on those two the shelf multiplied by the printed size without dividing by the width. The Miura's folding length was reported as 6,679 millimetres and is 1,049, and the same pattern's printable sheet has carried the right number all along.

material · Crease density

Named alongside it

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

Crease patternAssignmentAttributionCrease densityCrease lengthFold formatFolded stateLayer orderingMeasurementNotationSystematic error

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