Folding concentric accordion pleats results in a shape that collapses into a approximation (called a Hypar, by Bauhaus architects who folded it in the early 20th Century) of a saddle shaped surface (a manifold mathematicians call a hyperbolic paraboloid). A cycle of four edges traces out a Hamilton Cycle of a tetrahedron's edges. Thus, a square-based hypar fits well inside a tetrahedral frame. We will make a frame from 6 of the late Francis Ow's 60-degree modular unit (a version of which is the same tetrahedron used five times in the Five Intersecting Tetrahedra model by Tom Hull, though assembling that 30-unit model is outside the scope of this class). One square sheet is needed for a square-based hypar, plus three more squares of the same size (to each be cut in half) for the 6-unit tetrahedral frame. 15cm kami works well, as does 75mm kami with sufficient precision. Sturdier paper (such as printer paper cut into four equal squares) will hold the form better, but is not required.
- Uses cuts.
- This uses non-square paper: The tetrahedron is made from narrower rectangles (half squares).
- This is a modular/composite requiring 4 sheets.
- The interior saddle-shaped surface is a corrugation.
The saddle-shape can be made at different resolutions, depending on the skill and ambition and time available to the folder.
It is possible some students might take longer than the allotted time, especially if they want a higher-resolution hypar, which can be improved upon outside of class. Some students might want to try folding a second frame from narrower strips. Other suspected time-hazards are rectangle-cutting and tetrahedron assembly.
Francis Ow's 60 Degree Unit:
https://owrigami.com/show_diagram.php?diagram=60unit
Tom Hull's Five Intersecting Tetrahedra, another model that uses Ow's 60-degree unit:
http://origametry.net/fit.html
Some background on the square Hypar (and related models):
https://erikdemaine.org/curved/history/
More info specifically about Josef Albers, whose class (possibly a student or students) might have originated the hypar model:
http://www.origamiheaven.com/historyjosephalbers.htm
Some photos of a rendition of just the square-based hypar:
https://origami.kosmulski.org/models/hypar-clean
Four (or three) squares the same size, and a means of cutting three of them in half (bring your own scissors, or cut in advance), or one square and six 1:2 (or 1:3) rectangles cut from the other three (or two) squares. Suggested starting size is (4 differently-coloured squares of) 15cm kami.