MOD58 - I-SQUASH-A-HEDRON - A SIX-UNIT ACTION MODEL BY DAVID BRILL (USING 6 RECTANGLES)

Credits and Resources:
Design: by David Brill - © 2018
A PDF diagram for this model is available from the following link: brilliantorigami.com
A video tutorial by Sara Adams of happyfolding.com is also available on youtube.com
Text Tutorial: © 2026 by Lindy van der Merwe and accessorigami.com
With special thanks to James Peake of Foldspace Origami Studio foldspacestudio.com and to Annette Carr for test-folding and editing suggestions.

Steps: 35
Folding Level: Beginner to Intermediate

Description: This modular creation is a moving six-unit construction, forming a cuboctahedron in its closed position.
We can also think of it as a "truncated" cube or a cube with its corners sliced off.
It is able to expand into a larger, much rounder shape with a simple pulling motion and is easily returned to its smaller, closed state.

Terminology
Corrugation folding (tangentially related to Miura-ori, named after Japanese astrophysicist Professor Koryo Miura): This technique involves creating multiple accordion pleats and then installing angled creases through all the layers to make a collapsible, zigzag pattern.
First-Degree Creases: The initial parallel accordion pleats.
Second-Degree Creases: The angled creases that cross and reflect through the first-degree pleats.

Paper to be used: 6 2x1 rectangles cut from 3 20 cm squares.
You will also need 6 paper clips.

Phase 1 - Folding Your First Unit

Part 1 - Initial Pre-Creasing (First-Degree Pleats)

Step 1 - Short Pleat Folds

With one of the short sides of the rectangle nearest you, fold the bottom edge up to meet the top edge.
Crease and leave folded.
Fold the front layer of the paper down again, to meet the bottom, hinged edge of the model.
Crease and leave folded.
Flip the figure over from left to right.
Repeat the previous fold on this side of the model.
Open the paper completely and place it in landscape orientation, short edges on the left and right.

→Result: You should now have a rectangle divided into four equal sections by 3 vertical crease lines.
Don't worry about whether these lines are valley or mountain folds at this point.

Step 2 - Long Pleat Folds

Repeat the accordion-folding process by bringing the long bottom edge up to meet the top edge.
Then fold the front layer of the paper down, turning over and repeating the folding down step on the back.
Keep folded.

→Result: You should now have a long, thin multi-layered strip.

* Important: Before continuing, make sure that your long strip lies in front of you from left to right, with its raw edges facing away from you.

Part 2 - Angled Pre-Creasing (Second-Degree Creases)

Step 3

You will have three vertical crease lines across your rectangular strip.

Using the right most vertical crease, mountain fold the right most segment of the rectangle so that it is behind the model and the right most vertical crease becomes the new right short edge.
Crease well and leave folded.

→Result: We now have a hinged, straight right edge to help us with our next diagonal fold.

Step 4

Next, take what will now be the front layer of the strip and valley fold it diagonally upwards so its bottom edge will align with the right vertical edge you have just created.
The part of the strip you have folded upwards in this step will now be pointing in a straight line, away from you with the piece you have folded behind still in a horizontal position.

→Result: You will have created a 45 degree corner on the right.
Try to make this 45-degree angle as accurate as possible since it is important for the proper formation of the unit.
You are folding through many layers, so make a really strong crease.

Step 5

Unfold the previous two steps so you have the long rectangle again.

Step 6

Flip the strip over from left to right, making sure the raw edges are still facing away from you.

Step 7

Repeat Steps 3, 4 and 5.

→Result: Your long multi-layered strip will now have two diagonal creases through all its layers.
The arch shape you have now is what we will be aiming for in the next steps, but with the layers of the paper rearranged.

Part 3 - Reversing Mountains and Valleys

* Explanation: In this part of the tutorial, we are going to fold our model downwards at a 90-degree angle to get the arch shape again, but this time we will use all the fold lines to collapse this side of the shape so the pleats are arranged in a nice, symmetrical pattern.
In essence, we will be forming inside-reverse folds to create the first part of the arch shape.

Step 8

Pick up and open the paper slightly, turning it so one of the short edges is facing you.
Starting from the edge nearest you, find the fairly short zigzag or diagonal creases that will be located just past the first horizontal crease line you encounter.
All four of these short, diagonal creases should be turned into mountain folds.
Next, turn the long center vertical crease into a valley fold, while the left and right shorter vertical creases should be formed into mountain folds.

→Result: Once all your folds have fallen into place, you will be able to place the strip flat on the table again.
While the inner corner of the fold will be at a 90-degree angle, the outer edge of the figure will have a slanted, diagonal corner.

Step 9

Flip the model over from left to right.

Step 10

Repeat Step 8 to transform the remaining short end of the strip so it will form another 90-degree corner.

→Result: Your model is once again flat on the table, but now forming an arch, with two pillars or "legs", one on the left and one on the right.
* Note: We will call this arch or the horizontal part of the model the "central bar".

* Important: Before continuing, ensure that both inside corners of the model are folded at a 90-degree right angle.

Part 4 - Forming the "House" Shape

Step 11

Focus on the right "leg" of the model.
Open the paper like you would open a book to reveal a flat "house" shape that will be made up of a square with a right-isosceles triangle roof.

Step 12

Fold the bottom edge of the square of the "house" up to the line where the slope of the roof starts.
We can think of this as turning the two-storey house into a one-storey house.
Crease and leave folded.

Step 13

Flip the unit over from left to right and repeat Steps 11 and 12 so you have another one-storey house.

Step 14

Pick up the unit from your folding surface and swivel both the "house" shapes to the left and then to the right a few times to ensure they will be able to move perpendicular to the central bar in both directions.

Step 15

Hold the unit so the central arch or bar is at the top, running in front of you from left to right and so the house shapes seem to hang down from it on the left and right.
Swivel the house on the right so it is perpendicular to the central bar.
This means that the "front" of the house will face to the right now.
Similarly, swivel the house shape on the left so it will also be at a 90 degree angle/perpendicular to the central bar.
The front of this house will face to the left.
Your unit has now taken on its basic 3D shape, with only one step remaining.

Step 16

Rotate the unit so you are looking at the front of one of the house shapes.
Keeping the roof of the house so it stays at a 90 degree angle in relation to the central bar, fold the multi-layered "house" away from you as far as it will go, using a mountain fold.
This accordion-like fold will be stopped by the central bar or arch of the unit.
Crease and leave folded.

Step 17

Rotate the unit so the remaining house shape is now facing you and repeat the previous step.

→Result: What were the multi-layered house shapes will now both be folded underneath the central bar of the unit, reminding one a little of a jumping frog model.
You will be able to place it on the table so it is resting on the multi-layered flaps, which will become the tabs of the units.
There will be a triangle on each side, connected by the central bar of the unit.
With your unit in this position, the pocket will be hidden.
Only once you pick it up and start to swivel the tabs away from the central bar, will you have access to the pockets, which is located on the inside or underneath the central bar of each unit.
Your first unit is now completed.

Phase 2 - Folding More Units

Fold five more similar units.

Phase 3 - Assembly

* Explanation: Before starting your assembly, note the following:

Each unit has two tabs and one pocket.
The first storey or bottom part of the folded "house" will serve as the tab, and the opening on the inside or underneath the central bar acts as the pocket for modular assembly.
Using paper clips for the assembly of this model is strongly recommended.
These tiny tools serve not only to hold units in place temporarily, but are also used for orientation during the assembly process.
Make sure to insert tabs into pockets all the way and secure each insertion immediately with a paper clip before moving on to the next step.
Keep in mind that, for this model, each pocket/central bar will end up having two tabs inserted into it, which means there will be a few steps where you will have to remove a clip, add a tab and replace the clip.
In general, remember to orient your units with their central bars on the outside as you do the assembly.
It is fine to move your model in different directions during the assembly, but to help with orientation, each time you attach a paper clip, keep hold of the bar and the clip in question with the fingers of one hand while exploring with the other hand.
This should make the assembly much easier.

Step 18 - Insert unit 2

Pick up your first two units and insert one of the tabs of unit 2 into the central bar of unit 1.
Make sure it is inserted all the way and add a paper clip to the bar of unit 1.

Step 19 - Insert unit 3

Take a new unit (3) and insert one of its tabs into the central bar of unit 2.
Make sure it is inserted all the way and add a paper clip to the bar of unit 2.

Step 20 - Connect tab into unit 3

Next, notice that the bar of the last unit (3) you added will be open, with no paper clip and almost next to it, you will find the unused tab of unit 1.
So, insert the tab of unit 1 into the central bar of unit 3.
Make sure it is inserted all the way and add a paper clip to the bar of unit 3.

→Result: The first corner of our model is done.
The central bar of each unit has one tab inserted into it and each central bar will have a paper clip attached to it.

Step 21 - Insert unit 4

Next, pick any of the central bars of the model and insert a new unit (4) into it.
You will have to first remove the clip from the chosen central bar, then insert the tab of the new unit, making sure the already-inserted tab does not dislodge itself.
Make sure the new tab is inserted all the way and reattach the paper clip to the bar in question.

Step 22 - Connect tab into unit 4

Next, notice that the bar of the last unit (4) you added will be open, with no paper clip and once again, almost next to it, you will find another unused tab.
So, insert this tab into the central bar of unit 4.
Make sure it is inserted all the way and add a paper clip to the bar of unit 4.

→Result: The central bar of unit 4 will have a paper clip but only one tab.

* Important: Keep hold of the central bar of this unit for the next step.

Step 23 - Insert unit 5

Take a new unit (5) and insert one of its tabs into the central bar of unit 4.
You will have to first remove the clip from the chosen central bar, then insert the tab of the new unit, making sure the already-inserted tab does not dislodge itself.
Make sure the new tab is inserted all the way and reattach the paper clip to the bar in question.

→Result: Unit 4 will now have a paper clip and two tabs inserted into it.

Step 24 - Connect tab into unit 5

Next, notice that the bar of the last unit (5) you added will be open, with no paper clip and once again, almost next to it, you will find another unused tab.
So, insert this tab into the central bar of unit 5.
Make sure it is inserted all the way and add a paper clip to the bar of unit 5.

→Result: You have just added unit 5.
Its central bar will have a paper clip but only one tab.

* Important: Keep hold of the central bar of this unit for the next step.

Step 25

Follow the central bar of the unit you are holding to find the unused tab of the unit.

Step 26 - Connect 2nd tab into unit 5

Just next to this open tab, you will find a central bar that already has a paper clip and a tab inserted into it.
Remove the clip and insert the tab into the bar of the unit in question.
Reattach the clip after insertion.

→Result: Unit 5 will now have a paper clip and two tabs inserted into it.

Step 27

Next, find and follow any of the open tabs on the model until you get to its central bar.
This bar will have only one tab so far.

Step 28 - Insert unit 6

Take a new unit (6) and insert one of its tabs into the central bar in question.
You will have to first remove the clip from the chosen central bar, then insert the tab of the new unit, making sure the already-inserted tab does not dislodge itself.
Make sure the new tab is inserted all the way and reattach the paper clip to the bar in question.

→Result: Unit 6 has been added.

Step 29

Lift unit 6 slightly, pulling it away from the main model, so you will have access to its central bar.

Step 30

Find the remaining two tabs that will be left on your assembly and gently bring them together so they touch each other.

Step 31

Holding both tabs together, insert them into the central bar of unit 6.
Add a paper clip to secure the insertion.

Step 32

Very carefully insert the last unused tab into the central bar that will already have a tab inserted into it.
Take your time with this step.
You should be able to use the already-inserted tab to help you, using it as a surface to work against.

Step 33

Once the last tab is inserted, carefully remove all the paper clips.

Step 34 - Squashing

Now, cup both hands around the model and slowly squeeze or squash the model down so the creases are coaxed to settle into place.
The "squashed" model is a beautiful cuboctahedron.

Step 35 - Expanding

Notice that, on each face of the cuboctahedron, what was the top of the central bar of the units, will form a small ridge that stands out slightly from the rest of the model's surface.
This is part of the design and is actually what will be used to expand our model into its larger form.

So, with your model squashed down as small as it will go, find one of the protruding bars or ridges on opposite sides of the model.
Hold the bars between your thumbs and forefingers and gently pull your hands apart, using a single, controlled motion.
The model should expand in all directions into an intricate, rounded shape.
To return it to its smaller form, simply bring your hands together again.
This motion will become smoother after a while.
Although you may feel that the model may fall apart the first time you perform the expanding action, the I-squash-a-hedron is not only interesting in many ways, but it is one of the more robust models around.

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Compiled: September 2026
This text is © 2026 by accessorigami.com and the authors.