Introduction: How to Make a Triangular Hexahedron Out of Paper (Sonobe Units)

About the Process

The art of modular origami (paper folding with multiple pieces of paper, often used to create 3D geometric shapes) has been enjoyed by all ages. It is an extremely diverse field, consisting of many models, from figures that can be made with 2 pieces of paper, to elaborate models assembled from over 100 "modules," or building units.

Many different unit styles have been invented, each resulting in a different assembly technique. The model in this guide uses Sonobe units--a building module named after its presumed creator, Mitsunobu Sonobe. They are easy to fold, and models constructed with them are generally very sturdy and should not need any glue to stay together.

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The Model

This guide instructs on the creation of a 3D geometric shape called a "triangular hexahedron," which is the simplest figure that can be constructed from Sonobe units. It will walk through the steps to make a single unit and continue on to the assembly of the model. The finished product looks like two 3-sided pyramids joined together at the base, and depending on the size of the paper used, the model may be bigger than a basketball or smaller than a pencil eraser.

Step 1: Supplies

Supplies needed:

- 3 square pieces of paper of the same size (post-it notes are not always an exact square, but they work.)

- A hard, flat surface to make folding easier and cleaner

- Optional: Coloring supplies if using white paper (crayons, markers, colored pencils, etc.)

Step 2: Other Notes

- If you are using white paper and want color in your model, now is the time to add it. Add your colors, design, or drawing to one side of the paper. The colored side should be facing downwards when making the unit.

- If using sticky post-it notes, start with the sticky side facing downwards.

- Remember, precision is important when making those folds!

Step 3:

You will be using 3 squares to make 3 units, so you may want to go through the steps with each sheet as you go on.

Take one piece of paper and fold it in half.

Unfold it.

Step 4:

Fold the edges to the middle line created in the previous step.

Unfold.

Step 5:

Fold the bottom left corner so its edges line up with the lines created in the previous step.

Rotate the sheet and repeat the fold on the opposite diagonal corner.

Step 6:

Fold the triangle shape in the bottom left corner until its edge lines up with the bottom line.

Rotate the sheet and repeat on the other corner.

Step 7:

Fold the edges to the middle.

Step 8:

Take the bottom right corner and fold it until it touches the middle of the top edge. You will know you did it correctly if the two edges align perfectly, resulting in a sharply-pointed corner.

Rotate the shape and repeat the step with the other corner.

Step 9:

Insert the corner from one of the "triangles" all the way into the "pocket" as shown in the picture. Rotate the shape and repeat the step on the other corner.

Opening the model slightly by inserting your thumb into the pocket (or a pencil tip with very small units) may make it easier to complete this step. The unit should lie flat once both corners are tucked.

Turn it over.

Step 10:

Turn the unit until one of the sharp points is pointed slightly to your right, as in the picture.

Step 11:

Fold the sharp bottom point to the blunt corner on the top right.

Turn the unit and repeat the step on the other side. Unfold.

Step 12:

You have a completed Sonobe unit.

Step 13:

Once you have three complete units, you are ready to build a triangular hexahedron.

The units will be numbered from here to avoid confusion.

1. Blue

2. Yellow

3. Pink

Step 14:

Take unit 1 and make note of its "pockets," indicated in the picture with solid red.

Step 15:

Insert one of the points of unit 2 into a pocket on unit 1.

Step 16:

Insert a point of unit 3 into the empty pocket on unit 2.

Step 17:

Insert the last point of unit 1 into the unused pocket on the unit 3. You may have to bend the point to get it into the pocket.

Step 18:

The model so far should look like one corner of a cube.

Step 19:

Turn the model so the inside of the "cube" is facing you.

Step 20:

Take the point of unit 1 and insert it into the pocket of unit 2 behind the cube's left "wall." You will have to bend the "wall" to do this.

Make sure the remaining two points are not on the inside of the model.

Step 21:

Insert the point of unit 3 into the last pocket of unit 1.

Step 22:

Carefully slide the last point of unit 2 into the last pocket of unit 3.

Step 23:

Congratulations! You have completed the triangular hexahedron. It is a sturdy model that can be thrown around with little damage and is also usable as a desk decoration, a small giftbox (with larger units), or even as a jewelry component (with very small units). Have fun and get creative!

Comments

author
bmayhew made it! (author)2015-12-15

fun!

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dwhiddon made it! (author)2015-07-01

Nice dstraction from work

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ZeroThompson made it! (author)2014-12-02

Very cool! And not too difficult. I made one for my daughter with a secret note inside. Maybe she'll find it someday. :)

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Alligator911 made it! (author)2014-11-06

Cool

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Alligator911 (author)2014-11-05

Good!

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Fernandod1 (author)2014-10-30

This is pretty good, but I cannot resist pointing out that this is not a "triangular hexahedron". Hexahedron is just another, fancier, name for a cube, and calling it "triangular" doesn't change it. "Hexa" comes from the Greek word for 6, because a cube/hexahedron has 6 faces. What you have constructed is a tetrahedron ("tetra" = 4, because it has 4 faces).

author
jlms (author)Fernandod12014-11-03

Hexahedron. No question about it. You can see 3 sides there, plus the on in which it is standing, plus 2 more you can't see.

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haiku-san (author)Fernandod12014-10-30

The finished model does indeed have 6 faces. It's two 3-sided pyramids joined together at the base. The next level up from this model IS a cube, however.

author
gare8421 (author)haiku-san2014-10-30

This is indeed a hexahedron, though not a regular hexahedran (cube). The photos do look like a tetrahedron, but the resulting volume has six sides made from 6 right isosceles triangles.

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gare8421 (author)gare84212014-10-30

And it's fun to make.

author
Matt54 made it! (author)2014-11-03

Awesome!

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bizzycrafter (author)2014-10-31

OK, I am still really confused. This still looks like a tetrahedron to me. Please clarify. Maybe if you attach a drawing showing the 6 sides - - or just indicate the six sides with arrows in the photo?? Thank you!

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mrpesas made it! (author)2014-10-31

Here's a family of 4.

I've been making these for a few years with my students.

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mrpesas (author)mrpesas2014-10-31

Forgot to add. If you want to do this on a large scale (with students).

Go buy full packs of colored paper (8.5" x 11")

Then take them to your local print store (Kinkos) and they can cut off the ends of the entire ream so that you have have square paper.

The small paper I got from a spiral notepad at Staples.

author
sjuntasaro made it! (author)2014-10-30

it easy

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vtferret (author)2014-10-30

Awesome! It's only a matter of time till my office is filled with these, muahaha.

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tomatoskins (author)2014-10-27

I love me some origami! I've never tried this before. Definately something to look forward to. I actually just compleated this little guy the other night while watching some tv. Took quite a few hours a a pair of tweasers.

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haiku-san (author)tomatoskins2014-10-30

Very nice! Honestly, the triangular hexahedron is a few levels down from your...icosahedron? I tend to store my units in hexahedron form until I have enough for one of those.

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tomatoskins (author)haiku-san2014-10-30

Oh, I didn't know that. I'm honestly fairly new to modular origami. I thought it was different because I fold the units a little differently. But I see how they form the same overall shape now. I love your level of detail! Great 'ible! I'm looking forward to more great things from you!

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makermike (author)2014-10-30

I can't see that this is anything other than a tetrahedron. Can you add a picture to show that it is essentially two tetrahedra with a common face? Thanks!

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sakid.khan made it! (author)2014-10-30

easy to make it. thanks

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spass made it! (author)2014-10-29

Pretty cool, pretty easy too. Thanks can't wait for my son to come home from school. He will love this.

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NamedJohnny (author)2014-10-28

wow very cool!

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Basement_Craftsman (author)2014-10-28

I know what I'm doing in class today. Thanks for sharing

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JaredDiS (author)2014-10-28

This is probably the coolest thing I've seen

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Kiteman (author)2014-10-28

This has got to be the easiest-to-understand modular origami project I've read in a while.

Looking forward to more structures.

author
JM1999 (author)2014-10-27

Very well done, especially the drawings on the paper to help understand the text.

Nice job!