Origami & Folding
what one sheet can do
How this site is made

The figure library — page 14

Every picture here is generated from code at build time. This is every generator, ordered by how many essays call it, each rendered at its defaults.

polyomino-foldings

1 essay — The map that is not a rectangle · 9 claims checked

Take a square out and the count goes upThe number of foldings of each map, against the number of stackings its squares could possibly take. A map with a cell missing has fewer squares and fewer creases, and fewer creases means fewer things that can interfere — so removing the middle of a three-by-three multiplies the count rather than dividing it.foldings, and the stackings they are drawn frommapsquaresfoldingsa strip of five55041.7% of stackingsa plus5120every stacking worksa tee5120every stacking worksa two-by-three6608.3% of stackingsa two-by-three, one gone54033.3% of stackingsone corner gone88482.1% of stackingsthe middle gone8801619.9% of stackingsthe full square913680.4% of stackingsthe bars are on a logarithmic scale, because the counts run over three orders of magnitude

ratio-map

1 essay — A property you can dial · 3 claims checked

The ratio is a surface, not a numberPoisson's ratio for a Miura fold across the whole design space: the panel slant along one axis, how far the sheet is folded along the other, every cell measured off the solved rigid folding by finite difference. Every value is negative and none of them is the same, which is the difference between a property of a material and a property of a mechanism.-0.02-0.02-0.03-0.04-0.06-0.10-0.19-0.49-0.05-0.06-0.07-0.10-0.15-0.23-0.43-1.01-0.10-0.13-0.16-0.21-0.30-0.45-0.81-1.79-0.20-0.24-0.30-0.39-0.53-0.79-1.36-2.93-0.34-0.41-0.50-0.64-0.85-1.24-2.10-4.41-0.54-0.65-0.79-0.99-1.31-1.88-3.13-6.48-0.80-0.94-1.14-1.42-1.87-2.64-4.36-8.950.120.200.300.420.550.700.850.080.200.320.440.560.680.800.90panel slanthow far the sheet is closedwhat the map saysevery cell negativefrom -0.02 to -8.95a factor of 535.6a material has one value;this has a working point,and it is chosendarker means more negative

record-subjects

1 essay — Two kinds of claim · 3 claims checked

Two populations, and a median that describes neitherEvery claim in the record, placed by how far its usual date runs ahead of the oldest thing that attests it, and grouped by what sort of thing the claim is about. Claims about practices all run ahead; claims about results mostly run behind, and scatter far less.each mark is one claim: right of the line means dated earlier than its evidencethe vertical line is agreement between the claim and the record0paper itselfwhen and where the material was made, which is archaeologymedian 0 · spread 204a thing people dida fold, a ceremony, a toy, a lesson — something with no first daymedian 347 · spread 979a thing somebody proved or designeda statement with a paper, a date and an authormedian -14 · spread 131

ridges-and-hinges

1 essay — From a packing to a crease pattern · 4 claims checked

From a packing to a crease patternThe discs say where the flaps are; the creases say where to fold. A hinge crease is the common tangent where two discs touch, perpendicular to the line joining their centres and passing through the point of contact. A ridge crease bisects the corner of the region left between them. Both are computed from the packing here, and the contact geometry is asserted rather than drawn by eye.what the packing gives5 discs, 4 contactsno two overlapping, checkedhinge creasesone per contact, perpendicularto the line of centresridge creasesalong the axial lines, dividingthe paper between the flapsthe packing is the hard part;this part is a constructioncorner discs of radius 0.28, the middle one 0.427 — every contact measured

vertex-stackings

1 essay — One marking, many objects · 4 claims checked

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