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Sturdy Edge Module (StEM) — folding instructions

These are folding instructions for the Sturdy Edge Module (StEM) designed by me and independently by many others before me.

This unit is derived from Simple Edge Unit (SEU), so many of SEU's properties also apply to StEM. Compared to SEU, it is a bit more complex to fold and the modules are harder to connect, but it offers a number of advantages in exchange. The link between units is stronger and can usually be folded with a neater finish, which is especially visible when faces of a polyhedron meet at very acute or very obtuse angles. StEM can be folded from paper of any aspect ratio, but was designed with square paper in mind. Square paper results in an edge module which is quite bulky and has, in my opinion, better-looking proportions than SEU folded from 2:1 paper which looks a little skinny. Square paper is also closer in line with the classical origami rules.

StEM is a very versatile module which can be used to make a number of quite different objects. Three units can build a triangular 45 degree pyramid, so anything that can be made with Sonobe units can also be made with StEM. In addition, objects with square, triagonal and hexagonal faces can be made. Since the hole in the middle of the square face is ⅓ of the edge length, this unit is well-suited for making Menger Sponges. In most uses, StEM is an edge unit, but when folded in half along the shorter axis, it can be used as a face unit which behaves quite a bit like Sonobe unit (alternatively, you can see it still being an edge unit but with the edge going along the shorter instead of the longer axis of the module).

The pictures (diagrams) below are available under a Creative Commons license.

History and independent discovery by others

I designed this unit in November 2014 and published it in December 2014. This unit is quite simple and after designing it, I learned that it had been independently discovered by others before. In particular, Dirk Eisner came up with the same design, and others may have as well. 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.

In January 2015 when looking for potential prior art for this unit, I stumbled upon Carmen Sprung's modular icosahedron design. Her unit was published in 2002 and is very similar to StEM: it looks like a StEM unit folded from square paper with some additional creases. The folding sequence is different from mine even though it leads to a similar final form. Her version uses only square paper and can only be used to make triangular faces. It seems that the additional creases prevented her from seeing the full potential of the “partially folded” form which would be StEM.

Finished module (with inward/outward finish) and sample usage

Sturdy Edge Module (StEM) variant for inward-pointing triangles Sturdy Edge Module (StEM) variant for outward-pointing triangles Sturdy Edge Module - simple polyhedra: tetrahedron, cube, two octahedron variants Sturdy Edge Module - rhombicuboctahedron Sturdy Edge Module - truncated cuboctahedron Sturdy Edge Module - 14-spoked wheel / tetradecagonal prism Sturdy Edge Module - Robert Lang’s Annapurna (ten intersecting triangles)
Sturdy Edge Module - icosahedron with inverted spikes Sturdy Edge Module - spiked icosahedron Sturdy Edge Module (face unit variant) - spiked icosahedron Sturdy Edge Module (face unit variant) - icosahedron with inverted spikes Sturdy Edge Module - Menger Sponge Sturdy Edge Module - ring / closed band

Comparison between SEU and StEM units

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.

Rhombicuboctahedra - comparison between Simple Edge Unit (left) Sturdy Edge Module (right) Truncated tetrahedra - comparison between Simple Edge Unit (left) Sturdy Edge Module (right)

Folding the Sturdy Edge Module

StEM folding instructions

1. Start with a square piece of paper.

StEM folding instructions

2. Pleat the square, dividing one side into four equal pieces: first valley fold in half and then mountain fold into halves again.

StEM folding instructions

3. Collapse along the creases. Place the model with two free edges pointing North.

StEM folding instructions

4. Make a crease to divide the width in half. The crease need only go to about 1/3 of the module's length.

StEM folding instructions

5. Unfold along the main axis and rotate the unit.

StEM folding instructions

6. Valley fold so that the edge of paper lies along the crease created in previous step.

StEM folding instructions

7. Replace the valley fold with an inside reverse fold.

StEM folding instructions

8. Unfold the little corner.

StEM folding instructions

9. Repeat steps 4-8 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.

StEM folding instructions

10. Crease flaps.

StEM folding instructions

11. 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.

StEM folding instructions

12. Crease flaps for more convenient connection of modules later on.

StEM folding instructionsStEM folding instructions

13. Unfold. Finished module for outwards poiniting triangles is shown on the left, for inwards-pointing triangles on the right. Many other minor variations are possible and may be required for specific models.

Assembling the modules

Similar to many other edge units, StEM modules 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. Additional folds allow the module to be connected into thin and long "belts". You can find some examples of assemblies using this module at the top of this page.
StEM folding instructions

14. Connecting the modules using flaps.

StEM folding instructions

15. Flaps fully inserted.

Normally, as in the assembly examples above, StEM is used as an edge unit. However, it can also be folded in half along the shorter axis and used as a face unit. In this setup, it is similar to a Sonobe unit whose sides were cut off. An example of this connection method can be seen in the Toshie's Jewel below.
StEM folding instructions

Toshies Jewel, demonstrating the use of StEM as a face unit.

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