Origami & Folding
what one sheet can do
Generator

How many objects one marking makes

A generator in the flat-folding library, called 6 times across 1 essay. 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.

vertex-stackings 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

How many objects one marking makesFor each named vertex: how many mountain-and-valley labellings fold, how many of those produce exactly one stacking of the sectors, and the largest number of stackings any single labelling produces.of the markings that fold, how many folded objects each one makesmarkings that foldexactly one objectthe most any one makesthe preliminary base4 creases · four equal sectors, the first vertex anybody folds881a halved four-crease vertex4 creases · degree four with its two smallest sectors equal — the case the lemma is silent at661the waterbomb tessellation's odd vertex6 creases · degree six, and this site prints nine of them on one sheet18126a Yoshimura vertex6 creases · degree six with every sector equal, and twenty-two of them on the printed pattern30122the preliminary base's centre8 creases · degree eight, and the vertex at the middle of the first base anybody folds112164a vertex at no particular angles6 creases · degree six, drawn from the census and rounded to a tenth of a degree881at four creases the marking names the object; above it, it need not

view: "counts"

How many objects one marking makesFor each named vertex: how many mountain-and-valley labellings fold, how many of those produce exactly one stacking of the sectors, and the largest number of stackings any single labelling produces.of the markings that fold, how many folded objects each one makesmarkings that foldexactly one objectthe most any one makesthe preliminary base4 creases · four equal sectors, the first vertex anybody folds881a halved four-crease vertex4 creases · degree four with its two smallest sectors equal — the case the lemma is silent at661the waterbomb tessellation's odd vertex6 creases · degree six, and this site prints nine of them on one sheet18126a Yoshimura vertex6 creases · degree six with every sector equal, and twenty-two of them on the printed pattern30122the preliminary base's centre8 creases · degree eight, and the vertex at the middle of the first base anybody folds112164a vertex at no particular angles6 creases · degree six, drawn from the census and rounded to a tenth of a degree881at four creases the marking names the object; above it, it need not

view: "stack", slug: "yoshimura"

One marking, 2 folded objectsThe loop of paper round the vertex, folded onto a line. Each column is a legal stacking of the same sectors under the same mountain-and-valley letters: the horizontal extent of each bar is where that sector lands, and its height in the column is where it sits in the stack.a Yoshimura vertex, marked MMVVVV2 stackings satisfy every rule; 2 of them are drawnstacking 1stacking 2the crease pattern is the same in every column, and so is every letter on it

view: "stack", slug: "rosette"

One marking, 4 folded objectsThe loop of paper round the vertex, folded onto a line. Each column is a legal stacking of the same sectors under the same mountain-and-valley letters: the horizontal extent of each bar is where that sector lands, and its height in the column is where it sits in the stack.the preliminary base's centre, marked MMVVMVVV4 stackings satisfy every rule; 3 of them are drawnstacking 1stacking 2stacking 3the crease pattern is the same in every column, and so is every letter on it

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.

One marking, many objects

A crease pattern with every mountain and valley written on it is spoken of as though it named a folded model. At four creases it does. At six it need not, and at the eight-crease vertex in the middle of the first base anybody folds, a single marking can be folded into four genuinely different objects — same creases, same letters, four answers.

All the figures · The flat-folding field · The patterns a reader can fold