Origami & Folding
what one sheet can do
Concept

Facet — where it appears

A flat piece of a folded sheet, bounded by creases and by the paper's edge, that stays rigid while everything around it bends. A crease pattern's facets are what a folded state has to place, and the number of them is what most costs here are counted in.

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

24681012foldsinterior verticesfacetscrease lengththe median facet falls from 2.6e-1 to 4.0e-3 of the sheet

Every facet is a layer

Fold a sheet at random as many times as patience allows, then count three things: the creases it carries, the facets they cut it into, and the layers in the stack. The last two are the same number, always, and it is one more than the first — so how deep a crumpled sheet folds can be read off the flattened pattern without folding anything.

material · Crumpling each point is one pattern: panels across, nodes up00202040406060one node per panelnodes visitedpanels3 folds to 8 folds, and not one backtrack anywhere in the family

A crumple has no tail

The least structured crease pattern this collection can produce is a sheet folded at random and flattened. Its consistent letterings get rarer as it deepens — thirty-four of forty down to eleven — and finding one costs one step per panel from beginning to end, with no wrong guess anywhere. Disorder and difficulty turn out to be unrelated quantities.

material · Crumpling

Named alongside it

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

IdealisationAssignmentConservationConstraint propagationCountingCrease patternCrumplingLayer orderingSamplingSearch costSimple fold

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