Origami & Folding
what one sheet can do
Generator

Thickness that does not move the hinge

A generator in the rigid folding 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.

offset-panels 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

Thickness that does not move the hingeThe same fold given real thickness two ways, in cross-section. Growing each panel symmetrically about the ideal surface makes the two sides of every crease fight for the same space. Offsetting each panel entirely to one side leaves the hinge axes exactly where the zero-thickness pattern put them, so the mechanism moves along the ideal path — and pays for it by no longer being a surface.grown symmetricallyoffset to one sidepanels overlap over 4% of their areawhich is the jam every thick-panel design meetspanels do not overlap at alland the hinge axes have not movedwhich is not free: fold it tighter and this offset runs out toosheet 0.16 panel-lengths thick, folded to 100° — the overlap is measured from the geometry

thickness: 0.16, angle: 100, panels: 5

Thickness that does not move the hingeThe same fold given real thickness two ways, in cross-section. Growing each panel symmetrically about the ideal surface makes the two sides of every crease fight for the same space. Offsetting each panel entirely to one side leaves the hinge axes exactly where the zero-thickness pattern put them, so the mechanism moves along the ideal path — and pays for it by no longer being a surface.grown symmetricallyoffset to one sidepanels overlap over 4% of their areawhich is the jam every thick-panel design meetspanels do not overlap at alland the hinge axes have not movedwhich is not free: fold it tighter and this offset runs out toosheet 0.16 panel-lengths thick, folded to 100° — the overlap is measured from the geometry

thickness: 0.16, angle: 100, panels: 5

Thickness that does not move the hingeThe same fold given real thickness two ways, in cross-section. Growing each panel symmetrically about the ideal surface makes the two sides of every crease fight for the same space. Offsetting each panel entirely to one side leaves the hinge axes exactly where the zero-thickness pattern put them, so the mechanism moves along the ideal path — and pays for it by no longer being a surface.grown symmetricallyoffset to one sidepanels overlap over 4% of their areawhich is the jam every thick-panel design meetspanels do not overlap at alland the hinge axes have not movedwhich is not free: fold it tighter and this offset runs out toosheet 0.16 panel-lengths thick, folded to 100° — the overlap is measured from the geometry

angle: 60, thickness: 0.16

Thickness that does not move the hingeThe same fold given real thickness two ways, in cross-section. Growing each panel symmetrically about the ideal surface makes the two sides of every crease fight for the same space. Offsetting each panel entirely to one side leaves the hinge axes exactly where the zero-thickness pattern put them, so the mechanism moves along the ideal path — and pays for it by no longer being a surface.grown symmetricallyoffset to one sidepanels overlap over 7% of their areawhich is the jam every thick-panel design meetsoverlap down to 5%and the hinge axes have not movedwhich is not free: fold it tighter and this offset runs out toosheet 0.16 panel-lengths thick, folded to 60° — the overlap is measured from the geometry

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.

Error is folded too

A folded position is a composition of reflections, and a reflection in a line that is slightly off turns everything beyond it by twice as much. So an error does not stay where it was made — and whether it grows with the crease count or with its square root depends on whether it is the same error every time.

From a shell to a solar array

The Miura fold was published in 1970 and flew on a satellite in 1995. The gap is not ignorance — the pattern was known, understood and available the whole time — and the same twenty-five year lag appears between every folding result and the hardware that uses it.

Panels with somewhere to go

Every way of giving a folded panel real thickness costs something. Tachi's offset-panel technique costs the least interesting thing there is — it stops the panels being a surface, and leaves the hinges exactly where the zero-thickness pattern put them.

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