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Simple Edge Unit (SEU) — folding instructions
These are folding instructions for the Simple Edge Unit (SEU) designed by me and independently by many other people before. SEU is an edge unit with several interesting properties. In particular, it can be folded from paper of any proportions and when folded from a square sheet, it becomes a peculiar variant of Sonobe unit.
Of course you are free (and encouraged) to use it for folding your models and to use it as an inspiration when inventing your own modules.
History and independent discovery by others
This module is very simple. While I came up with it myself, I later learned that many others invented it independently. I would like to thank Dirk Eisner who provided me with references to other places where this unit was published. In particular, this unit has been independently discovered by: Francis Ow, Tomoko Fuse, Dirsk Eisner, myself, and probably a bunch of other people, too.
I first came up with this unit in late 1999 or January 2000 after learning of Francis Ow's 60 degree module (scroll down the linked page for unit folding instructions). However, since I was only starting my adventure with modular origami back then, I failed to see this 90-degree module's potential. I only folded a couple of cubes and thought that was it. I forgot about this unit for many years until it surprisingly came back to my mind in late 2014. At this point I instantly noticed that there were many more possible ways of connecting these units, for example that this module could be used for making triangular faces (which allows for pentagonal and hexagonal pyramids, too), pointed spikes etc. Using paper with differing proportions makes it possible to fold faces shaped like the "large" polygons: octagons and hexagons, and when folded from square paper, this unit becomes an interesting Sonobe variant (see below).
After re-inventing this unit the second time, I not only learned that the same unit had been discovered by others before but I also found a number of units which are similar but not exactly the same. These include the classical Sonobe module, Tomoko Fuse's Open Frame II, Tomoko Fuse's Double Pocket Unit, and M. Mukhopadhyay's Star Windows.
The pictures (diagrams) below are available under a Creative Commons license.
Folding from paper of different aspect ratios and relation to Sonobe unit
This unit can be folded from paper of any aspect ratio. 2:1 paper is convenient due to the ease of preparing such sheets from square paper, but it results in a somewhat skinny module. Paper with A4 proportions (1 to square root of 2), common in Europe, results in a module with proportions which I find close to perfect.
The angle between this unit's main axis and the edge of the flap is 45 degrees, so you can fold flat faces of square shape. As with many similar edge units, you can also fold triangular faces from this unit, in which case you can make the module's sides point either inwards or outwards. Choosing either variant requires minor changes in the way the units are folded.
When folded from 1:1 paper, this unit becomes a variant of Sonobe. A peculiarity of this variant is that the module's pockets extend all the way to the module's edges. This results in a very stable connection which makes it easy to fold models with high-tension angles. Additionally, one can use either the deep pockets or use the crease on the back face of the module as a pocket and connect the units in several different ways. This is a very nice property since one can create assemblies which look quite differently without modifying the units or their relative composition at all, only by using different connection methods.
Below you can see four different ways of connecting the Sonobe-like variant of SEU unit. Close-ups of individual unit links can be found below, at the end of "folding" section.
From left to right, these connection methods are:
- SEU link — flaps are inserted into the large pockets, as they would be in units made from elongated paper sheets.
- Reversed SEU link — modules are connected like in regular SEU link, but the reverse faces of modules are on the outside of the model, which results in small creases being visible in the finished model.
- Sonobe link — modules' reverse faces are on the outside of the model and flaps are inserted into the crease, resulting in a pattern similar to those found in other Sonobe variants.
- Rotated link — instead of valley folding each square's diagonal, thus each module making up one face for each of two adjacent triangular pyramids, the module's diagonal is mountain-folded and each module builds one edge of a single triangular pyramid. Thus, the number of units needed for a model is twice as high as for the previously mentioned connection methods. Each module only participates in one pyramid, so each paper patch on the surface of the model can be a different color (like in the example picture) while with the other linking methods, two adjacent patches always share the same color since they are formed from parts of a single module.
Finished module and sample usage
The finished module pictures are, in order: 2:1 paper (triangles pointing inwards), 2:1 paper (triangles pointing outwards), 1:1 square paper (Sonobe-like variant). Sonobe-like variant can also be folded for assembly with inwards- or outwards-facing pyramids.
Assembly examples in the picture with multiple polyhedra were folded from 2:1 and 1:1 paper. Notice how the tetrahedron made from Sonobe-like variant of the module becomes a cube. Some bending is visible in the truncated tetrahedron model - this is one of the deficiencies in SEU made from high aspect ratio paper which the Sturdy Edge Module solves.
Other examples are made from different paper proportions, including 2:1, 1:1 square paper (Sonobe-like variant) and 1:√2 (A4 paper proportions).
Comparison between SEU and StEM units
From the Simple Edge Unit, I derived another module, the Sturdy Edge Module (StEM) in order to deal with some deficiencies of the original design. StEM is a bit more complex to fold, but has a stronger link and different width-to-length proportions when folded from square paper.
In each of these pictures, the model on the left was folded from SEU units made of 2:1 paper and the model on the right was folded from StEM units made of 1:1 paper.
Folding the Simple Edge Unit
Instructions show 2:1 paper but this module can be folded from paper of any proportions. If you start with a square piece of paper, you will get a Sonobe-like variant of the unit.
1. Start with a rectangular or square piece of paper (2:1 shown in the instructions).
2. Pleat, dividing the shorter side into four equal pieces: first valley fold in half and then mountain fold into halves again.
3. Collapse along the creases.
4. Unfold the middle crease, rotate the model as shown in the picture.
5. Valley fold the module's corner, forming a 45-degree angle (top edge should be aligned with left edge).
6. Replace the valley fold with an inside reverse fold.
7. Tuck the little corner inside.
8. Repeat steps 5-7 at the other end of the module. In practice it may be more convenient to perform each of these steps at both ends one right after another.
9. Crease flaps.
10. Fold along the main axis. For triangular faces, the module's sides may be made to point inwards or outwards and this will require this one and following folds to be applied in the opposite direction than shown. Images show folding for triangles pointing outwards.
11. Unfold. Finished module for outwards poiniting triangles is shown on the left, for inwards-pointing triangles on the right. The end-result of folding from square paper (Sonobe-like variant) is show below (this is for inwards-pointing triangles, outwards-pointing is also possible). Depending on how modules will be connected, it may be a good idea to add creases on the flaps to make the modules align better against each other. Many other minor variations are possible and may be required for specific models.
Assembling the modules
Similar to many other edge units, SEU units can be connected in many different ways. The angle between the axis and the tip is 45 degrees so a flat connection results in square faces. If squares are creased along their diagonals you can create spiky balls (like with Sonobe units). Eqilateral triangles can be made with the edge units pointing inwards or outwards, and triangles can be used to create pyramids which cover pentagonal or hexagonal faces. Many other connection methods are possible, like long, thin belts, and for the Sonobe-like version anything that is possible with Sonobe modules also goes here. You can find some examples of assemblies using this module at the top of this page.
14. Connecting the modules using flaps, for 2:1 paper and for square paper module variants. For square paper, there are several different ways of connecting the Sonobe-like units, resulting in different patterns visible in the finished model. Some examples are described at the top of this page, in section "Relation to Sonobe unit".
15. Flaps fully inserted (2:1 paper).