Origami & Folding
what one sheet can do
Concept

Deployable boom — where it appears

A long structure stowed short and extended in place, such as a mast or arm carried folded into space. Folded tubes like the Yoshimura and Kresling patterns are candidates because their length changes by folding alone, and clicking courses can hold a boom at more than one length without a lock.

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

the flat pattern6 columns · 5 rowsthe course, closedradius 0.16676 sides of 0.1667 close into a ring of radius 0.1667, in the sheet's own unitsthe circle through the corners is 4.72% longer than the ring, which is what a 6-sided polygonowes its circle

The cylinder the pattern chooses

A Yoshimura pattern folds into a tube, and the tube's diameter is not a property of the paper. The course of diamonds has to go round exactly once, so the sheet's width is spent on the circumference the moment the columns are drawn — and what a larger sheet buys is a longer tube, never a fatter one.

tessellation · Found patterns four courses of alternating hands, ends clamped, holding 0011a right-handed course and a left-handed one shut together, so the ends need not turnright-handed, made 1.30 H: openleft-handed, made 1.45 H: openright-handed, made 1.60 H: shutleft-handed, made 1.75 H: shut

Clamped, a stack counts in pairs

A Kresling tube of four courses, its ends free to turn, can be pressed and pulled into all sixteen of its words. Clamp the ends so they cannot turn and the courses stop being independent switches, because a course that clicks shut turns by a fixed angle — eighty degrees here, whatever height it was made at — and the others must give it back. With every course of one hand the stack does not click at all, at more than twice the force that shuts any course free. With two courses of each hand it clicks in pairs, one of each hand together, so that their turns cancel: every word it reaches has as many right-handed courses shut as left-handed, and it reaches exactly four. The clamp turns a sixteen-word register into a two-switch one whose every state leaves the ends where they were.

tessellation · Found patterns

Named alongside it

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

CylinderThe big-little-big lemmaClosureEnergy minimisationFound patternKawasaki's theoremSymmetryTaperThe Yoshimura pattern

All concepts