Origami & Folding
what one sheet can do
Series

Found patterns — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. found rather than designedcrushed drink cans, tree bark,deployable boomsat every interior vertexsectors 60°, 60°, 60°, 60°, 60°, 60°two courses and four diagonalstwo of one letter, four of the otherwhy the height is not freea steeper diagonal makes the topsector strictly smallest, flankedby two of the same letter20 interior vertices · 23 mountain and 56 valley creasesmountainvalleyraw edge

    Patterns nobody designed

    Crush a thin cylinder and it folds into a diamond lattice. Nobody chose the pattern — it is the buckling mode with the lowest energy, and it satisfies the flat-folding theorems because it just folded.

    part 1 · tessellation
  2. 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.

    part 2 · tessellation
  3. the folded period of the Yoshimuradrawn periods across the top1234567the turnsame way upslides240°yesno120°yesno0°yesyes240°yesno120°yesno0°yesyes240°yesnoa turn of 240° comes back to nothing after three of them, and that is the folded periodthe drawing repeats every one, which is what makes it a tessellation

    The period nobody measured

    Every repeating pattern in this collection has its drawn period recorded, because a drawing cannot be generated without one. Its folded period is recorded nowhere, and on one of the families measured the two differ by a factor of three — which means the number that has always been quoted is the wrong one for anything about the folded object.

    part 3 · tessellation

All series