The band a twist tessellation lives in
twist-bounds 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
kind: "square"
kind: "hexagonal"
kind: "triangular"
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.
- a larger twist has a lower floor, so the two fences move in opposite directions as the twist grows ×1
- and where it appears the two smallest sectors at a corner are within 2.78° of each other, which is the crossing ×1
- over 5 twist sizes the ceiling is above the floor everywhere, so the band the construction lives in is never empty ×1
- the hexagonal pattern has no assignment below 13.75° and one at every angle above it ×1
- the triangular pattern has no assignment below 13.75° and one at every angle above it ×1
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 no costs more than a yes
When a folding question comes back yes, it comes back with an object: a labelling, a stacking, a folded state that anybody can check in one pass. When it comes back no, it comes back with nothing but the assurance that a search looked everywhere — and that assurance is the first thing to break.
Fenced at both ends
The twist angle of a tessellation looks like a free dial, and it is fenced twice. Turn too far and the pleats have no paper left. Turn too little and something stranger happens: every angle condition in the subject goes on holding and the pattern loses its mountain-valley assignment entirely.
All the figures · The tessellations field · The patterns a reader can fold