SON04 - MODULAR ORIGAMI - OCTAHEDRON - (FROM 12 SONOBE UNITS)

Modular Origami - Octahedron

MODULAR ORIGAMI - OCTAHEDRON (FROM 12 SONOBE UNITS)
Text-Only Origami Instructions
Lindy van der Merwe and Nishi Sakpal
Copyright 2024 AccessOrigami.com

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1. Introduction

The octahedron is one of the five Platonic solids, the others being the hexahedron, the cube, the icosahedron, and the dodecahedron. You can read more about these fascinating geometric shapes at Cuemath.

There are many ways to construct these and other geometric shapes, with and without using glue or tape. In this tutorial, 12 Sonobe units are used to construct an octahedron. For text-based information on how to fold the Sonobe Unit, visit Access Origami. It’s suggested to start with structures of 3 and 6 units before moving on to 12 and 30 unit assemblies, as experience is valuable for more challenging modular assemblies. You will likely need a lot of time, patience, and some tenacity. It’s normal to grapple with constructions and return to them later. Understanding the concepts in this type of construction and developing fine muscle movement and memory will allow you to eventually construct geometric structures with ease.

Apart from their beauty and the challenge of construction using origami, hollow, round shapes like this one are great to use as decorations. You can also use them to hide a special surprise by adding the item before closing the structure.

Before continuing, take time to fold at least 24 Sonobe units that all look the same.

2. Terms Used

2.1. Octahedron
One of the five Platonic solids with 8 equilateral triangular faces, 12 edges, and 6 vertices. Picture the octahedron as two pyramids joined at their bases or as a round object with points sticking out. You will shape the model from the bottom, working in a circle from a center point, widening, and ending at another center point at the top.

2.2. Units
In this tutorial, 12 Sonobe units are used to create the octahedron.

2.3. Pointy flap or flap
Each unit has two points or flaps to be inserted into pockets of other units.

2.4. Pocket
The central area of each Sonobe unit has two pockets where the flaps of other units will be inserted.

2.5. Face
The outside of a structure. For a cube, you'll see 6 flat square faces; for the octahedron, 8 bent triangular faces.

2.6. Edge
While assembling, each unit will have an open edge with its pocket on the right and a pointy flap on the left.

2.7. Pyramid
The model is made by constructing "pyramids"—triangular shapes that stand out from the model’s surface.

2.8. Orientation
2.8.1. Working orientation
How you hold your model while inserting flaps, sometimes involving holding it in the air or placing it down temporarily. The "inside" of the structure faces you.
2.8.2. Flat orientation
The assembly is turned with its inside facing the table, opened and pressed flat. In this orientation, it’s easier to count pyramid structures as they stand up from the model’s flat surface. Ensure all pointy flaps are tucked in underneath the model when in the flat orientation.

3. Tips for Constructing the Octahedron

3.1. Paper Choice
Use paper around 6 x 6 inches with a rough texture. The paper should be rigid enough to hold its shape. Consider using very thin cardstock or thick construction paper.

3.2. Prepare Units
Fold enough units before starting assembly. It's suggested to fold double the amount needed. This helps with orientation, especially for beginners.

3.3. Accurate Folding
Fold as accurately as possible. Any slight misalignment in points and edges can cause problems during assembly.

3.4. Glue and Tape
Once practiced, no adhesive is needed. However, beginners may find glue or some kind of tape helpful while learning to construct the model. Be cautious, as glue or tape can make adjustments difficult and messy.

3.5. Unit Quality
If units are torn, tacky, or flat, start over with new ones. Compromised units can cause the model to lose shape and fall apart.

3.6. Springy Units
Ensure units feel springy. They should resemble an origami bird with wings open at a 45-degree angle. Add a diagonal crease from top left to bottom right. Fold it back and forth once or twice without overdoing it to maintain springiness.

3.7. Uniform Folding
Ensure all units are folded similarly, with pockets on the central square faces. If you omit tucking in the corners to lock the units before turning them over, you will find only a flat surface, with no pockets to use.

3.8. Marking the Center
Mark the bottom center point of the shape. Beginners may find it helpful to secure this point with glue tack for better orientation during assembly.

3.9. Work Area
Use a large tray with a small rim or a flat lid of a box. Keep units on one side and work on the model on the other.

3.10. Organize Units
Keep units in a container and take them out in groups.

3.11. Keep Count
Keep track of the units you insert and those remaining to better understand the row construction.

3.12 Follow Instructions
Do not insert any points other than those specified in the instructions, even if frustrated.

3.13. Diagonal Fold
Ensure all Sonobe units have a diagonal fold across the square. This is necessary for the hexahedron, octahedron, and icosahedron.

4. Construction - Row 1

Row 1 will have 4 pyramids radiating from a center point and will need 8 units. Think of it as a bowl-like formation with a small central hole surrounded by 4 pointy pyramids. The construction starts from the left and moves to the right in a circular shape.

4.1. Pyramid 1 (First Half Cube) - 3 Units

We will be adding units 1, 2 and 3 to form our first half-cube or pyramid.
Tip: To help you, you can sum this pyramid up as: Start with unit 1, add unit 2, add unit 3, join unit 1 at the back of unit 3.
Here are the detailed steps.

Action 1

Hold your first Sonobe unit with pockets facing away, flaps at the top and bottom. Let the bottom flap rest on the table.

Action 2

Hold unit 2 with flaps left and right, insert it into the right pocket at the back of unit 1. Hold them together.

Action 3

Take unit 3, hold with flaps top and bottom, coming from above, insert the flap of unit 3 into the back of unit 2.

Action 4

Bend unit 1 slightly to the right, insert it into the pocket at the back of unit 3. You should have a half cube with 3 connected square panels and 3 loose flaps.

Action 5

Fold in all flaps to lay flat against the inside sides of the half-cube.

Action 6

Reinforce Pyramid 1 by turning the assembly with the open side on the table (flat orientation). Feel a point standing up at the center, Pinch and press down to accentuate diagonal lines while flattening outer edges on the table.

Explanation 1

(a) Identifying faces Make sure you can identify the 3 faces of your pyramid in this orientation. One will be nearest you, another will be on the right and the last will be on the left. The faces will still be square, but they will now be in a diamond/like orientation with one part of each face standing up, forming the actual pyramid and the other part of each face will form a triangular point that is flat on the table.

(B) Identifying edges with pockets and flaps Trace the pyramid outline. It is six-sided. The face nearest you will have an open edge with a pocket on the right and a long flap on the left. This pattern is the same for the remaining faces.

Action 7

pick the pyramid up and turn it so it is in the working orientation again.
Pyramid 1 is done.

4.2. Pyramid 2 - 2 units

We will be adding units 4 and 5 to form this pyramid.
Tip: To help you, you can sum this pyramid up as: Add unit 4, add unit 5, join unit 5 on the right with unit 4.
Here are the detailed steps.

Action 8

Hold the structure in the working orientation and choose any open edge with its pocket. Turn the figure so your chosen edge with its pocket is facing away from you, so you are able to access this pocket coming from the right. We will call this unit 3.

Action 9

Hold unit 4 with its flaps on the left and right and insert it into the right pocket at the back of unit 3.

Action 10

Find the flap of unit 3, which should be standing up just to the left of unit 4. Hold it up, ready for the next step.

Action 11

Take unit 5 and, holding it with its flaps at the left and right, insert the flap of unit 3 into the back of unit 5.

Action 12

Now, bending unit 5 slightly to the right, insert it into the pocket at the back of unit 4. Once done, you will still have a structure that looks a bit like a lopsided cube.

Action 13

Keeping the points tucked against the inside of the figure, turn the assembly with its open side to the table. Carefully spread the model so that you can feel the pyramid shapes standing up. You should now feel 2 points standing up at the center of the structure. There should be one nearest you and another furthest away, with a straight line separating them, like a valley.
Pinch the new point between your fingers while pressing down on the structure, so that you can accentuate the diagonal lines of the model. Press down as much as the structure will allow. You want the outer edges of the figure to lie flat on the table. Look at the outline of your assembly. If you trace your finger around the shape, you will now find 8 outer edges. Put in another way, there will be 4 faces, each with a pocket and a flap.

Action 14

Note the face nearest you, on the right of the structure. You are specifically looking for the open edge with its pocket, since this is where you will be inserting your next unit. Once you find the diagonal opening of the pocket, keep hold of it when you turn the model over.

Action 15

Like you did before, turn the assembly back into the working orientation and place the figure so you are able to access the pocket you are holding, coming from the right.
Pyramid 2 is done.

4.3. Pyramid 3 - 2 units

We will be adding units 6 and 7 to form this pyramid.
Tip: To help you, you can sum this pyramid up as: Add unit 6, add unit 7, join unit 7 on the right with unit 6.
Here are the detailed steps.

Action 16

Make sure your assembly is in the working orientation with the flap you identified in the previous step on the far right. Alternatively, just hold the structure in the working orientation and choose any open edge with its pocket. Turn the figure so your chosen edge with its pocket is facing away from you, so you are able to access this pocket coming from the right. We will call this unit 5.

Action 17

Hold unit 6 with its flaps on the left and right and insert it into the right pocket at the back of unit 5.

Action 18

Find the flap of unit 5, which should be standing up just to the left of unit 6. Hold it up, ready for the next step.

Action 19

Take unit 7 and, holding it with its flaps at the left and right, insert the flap of unit 5 into the back of unit 7.

Action 20

Now, bending unit 7 slightly to the right, insert it into the pocket at the back of unit 6. You will find that your model is becoming longer, forming a kind of semi-circle now.

Action 21

Keeping the points tucked against the inside of the figure, turn the assembly with its open side to the table. Carefully spread the model so that you can feel the pyramid shapes standing up. You should now feel 3 points standing up at the center of the structure. Turn the shape so that one of the pyramids is nearest you with another behind it and the third should be furthest away from you - almost as if the 3 pyramids form a little train.
Pinch the new point between your fingers while pressing down on the structure, so that you can accentuate the diagonal lines of the model. Press down as much as the structure will allow. You want the outer edges of the figure to lie flat on the table. Look at the outline of your assembly. If you trace your finger around the shape, you will now find 10 outer edges.

Action 22

Find the place where there seems to be a triangular cut-out or gap when you trace the outer edge of the figure. Rotate the shape so that the gap is nearest you. In the next steps, we will be closing the gap you have identified, which will complete the bottom row or base of our octahedron.

Action 23

Now, gently take the figure on both sides and flip it over, away from you, so that the triangular gap is now on the side furthest away. Tuck down all the flaps you can find so they are flat against the inside of the shape. Your assembly is once again in the working orientation, but now it will look more like a bowl with 3 hollow compartments or divisions - one at the center nearest you, another on the left and the last, on the right.
Pyramid 3 is done.

4.4. Pyramid 4 - 1 unit

We will now be adding unit 8 to complete our ring or base of our octahedron.
Tip: To help you, you can sum it up as: Join units 1 and 7, add unit 8 and tuck it into the unit to its right.
Here are the detailed steps.

Action 24

You are going to close the gap by inserting the flap on the right into the unit on the left. Once the two edges are joined, the gap will be gone. Don't let go of the place where you have joined these two units. You will need the flap of the left unit that is standing up straight for the next step.

Action 25

Now, take the new unit 8 and hold it with its flaps at the left and right. Insert the point that you are holding from the previous step into the pocket at the back of unit 8.

Action 26

Lastly, tuck the right flap of unit 8 into the pocket on its right. It will feel a bit strange, as if you are bending the unit when you do this. However, once tucked in, your shape will be symmetrical.
Pyramid 4 is done.

Explanation 2

The base of the octahedron is now completed.

(A) Flat orientation Turn the model over, but do not press it flat like before. You will have something vaguely resembling an umbrella, with spokes radiating out from a center point. It will actually be a tiny hole, which you should try to keep as small as possible. This will be a nice reference point for you, though. There will be 4 spokes, each ending in a small triangular mountain. If you follow each mountain away from the center and downwards, you will find a square or diamond shape that ends at a point that will touch the table.

(B) Working orientation If you turn the shape back into the working orientation, there will be the following:
(1) On the inside of the bowl-like figure, a center point with 4 valley-like divisions radiating out to txxxhe edges.
(2) Along the outer or top edges of the structure, there will be an alternating pattern of 2 things: a folded flap, always angled to the right and a straight edge with a pocket on the outside of the shape. If you fold in all the flaps to the inside of the figure, touching it on the edge from the outside, there will be 4 triangles standing upright with their points facing the ceiling.
Now it is time to add the next units, making up row 2.

5. Construction - Row 2

Explanation 3

From hereon, you won't have to turn the model over anymore. You will simply be adding units while the figure is in the working orientation.
Note also that after pyramid 5 is described, the last steps for adding units 11 and 12 will not be referring to pyramids, since the construction of the second row is done differently from that of the first.
Simply follow the last few steps without worrying about which pyramid you are constructing.
Tip: To help you, you can sum this row up as: Add 2 units, join, add 1 unit, join, add 1 unit, join, close last 3 flaps.

5.1. Pyramid 5

We will be adding units 9 and 10 to form this pyramid.
Tip: To help you, you can sum this pyramid up as: Add unit 9, add unit 10, join unit 10 on the right with unit 9.
This is the same way you formed your second pyramid.
Here are the detailed steps.

Action 27

Hold the structure in the working orientation and choose any open edge with its pocket. Turn the figure so your chosen edge is furthest away from you, so you are able to access this pocket coming from the right. We will call this unit 8.

Action 28

Hold unit 9 with its flaps on the left and right and insert it into the right pocket at the back of unit 8.

Action 29

Find the flap of unit 8, which should be standing up just to the left of unit 9. Hold it up, ready for the next step.

Action 30

Take unit 10 and, holding it with its flaps at the left and right, insert the flap of unit 8 into the back of unit 10.

Action 31

Now, bending unit 10 slightly to the right, insert its right flap into the back of unit 9. Hold on to the flap of unit 9 that is standing straight up, for the moment.

Action 32

Just to the right of this flap, you will find an opening and to the right of the opening, another flap with its point to the left. Take the flap on the right, which will be from Row 1 and put it into the pocket just to the left of it. These two elements, namely the pocket on the left and the flap on the right, will already be adjacent to each other, so the join should feel quite natural and obvious.

Action 33

Find the next open edge with its pocket just to the right of the flap you have inserted.

5.2. Unit 11

Action 34

Hold unit 11 with its flaps on the left and right and insert it into the next pocket on the right.

Action 35

Find the flap standing up just to its left insert it into the new unit 11.

Action 36

Like before, just to the right of this flap, you will find an opening and to the right of the opening, another flap with its point to the left.

Action 37

Take the flap on the right, which will be from Row 1 and put it into the pocket just to the left of it. These two elements, namely the pocket on the left and the flap on the right, will already be adjacent to each other, so the join should feel quite natural and obvious.

Action 38

Find the open edge with its pocket just to the right of the flap you have inserted.

5.3. Unit 12

Action 39

Hold unit 12 with its flaps on the left and right and insert it into the next pocket on the right.

Action 40

Find the flap standing up just to its left and insert it at the back of the new unit 12.
All 12 Sonobe units have now been inserted.

6. Closing the Octahedron

At this point you should have added all 12 units. All that remains is to close the structure. Turn it so that the central starting point is at the bottom of the shape. You should have 3 loose flaps at the top opening of the model, which will form a final pyramid.

Action 41

Before continuing, gently reach inside the figure and bring all the flaps so their points lay on the outside surface of the model. Be careful not to dislodge any of these flaps at this time.

Action 42

Carefully press the figure closed so that the remaining flaps will overlap each other. Your octahedron will now have taken on its final shape, but with 3 flaps that still need to be tucked in. There should be no more open edges, holes or spaces. You will now be able to recognize where each of the 3 flaps should be tucked into their respective pockets.

Action 43

Take any one of the flaps and tuck it into its corresponding pocket. You might need a fingernail to open the pockets of the units now. You can bend the units near the top of the shape very slightly to help with the insertion of these last points, but be careful not to dislodge units lower down around the model.

Action 44

Repeat with the remaining 2 loose points. The last flap may feel a little difficult to insert, but just take your time while holding the entire structure securely in one hand.

Action 45

Once the last flap slots into place, you will be able to check your octahedron for any flaps that have not been tucked in and for obvious places where the shape may not have formed properly.
If all went well, you can now appreciate the beauty and symmetry of this amazing geometric shape.
If you are not happy with your result, remember it will take time to master this type of modular origami, so you may have to fold this shape multiple times before you will succeed.
Good luck and happy folding!

Making origami accessible through text-only instructions.

For non-commercial use only.

Compiled by Lindy van der Merwe and Nishi Sakpal - August 2024

>This text copyright 2024 by accessorigami.com

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