I have been fascinated by a transforming cube that I have had since I was a kid. For those of you not familiar with them, transforming cubes are toys with pictures on the inside that can unfold to reveal different surfaces each time. When the cube is fully unfolded, it creates a cube with a completely different surface than the original. However, this design can be modified so that when the cube is fully folded outward, it makes a completely new shape: a star (check the video above to see how this happens)!
Thus, I set out to create my own variant that could be reproduced from paper, which I titled the Geode Cube, because of its boring exterior color but beautiful internals (just like a real geode). I have also decided to give this template (and the PDO file) for free, and to give a brief walkthrough of how I created the model/template. The final object is a great toy to fidget with, keep on display, or even give as a gift. Made from only 3 sheets of paper, it is cheap to create and can be made by nearly anyone. It also has lots of room for customizability, and you can create it using any kind of paper you like (as long as it's sturdy enough).
The cube itself consists of 8 identical units, which I have called cubies. The cubies are held together by strategically placed strips of paper (I called them bonding strips), which allow the cube to unfold and turn inside out. Each cubie is very easy to assemble, as you will see, and I have provided very detailed instructions and 3D models to help guide you, so don't be shy to attempt this if this project will be your first papercraft!
Now, lets begin making!
Step 1: Creating the Design
For those of you only interested in making the model and not the design process, skip to the next step so you can begin. If you're interested in how I made it, keep reading!
To create the 3D model, I observed a normal transforming picture cube that I owned and boiled it down to 2 things: transforming cubes are made of 8 smaller cubes, and are bonded by 8 hinges. Thus, I would only have to create one cube and one hinge, and then duplicate each 8 times. However, to make a transforming star instead of a transforming cube, the inside of the shape must be different than the cube interior. After doing some research on some 3d printable transforming stars, I found a way to create the hidden star on the inside.
To make each sub cube, which I'm calling a cubie, I used Sketchup. First, I created a 2"x2" square, and extruded it upwards 2" to create a 2"x2"x2" cube. From there, I deleted the three front faces of the cube, exposing the insides. To make the hidden star shape, I drew lines to connect each of the opposite corners (see the pictures above). After that, the cubie itself is done! Too make the bonding strip, I simply drew a 1/2" by 2" rectangle. This is all that's needed for the units. From there, I exported the objects as a .DAE file (Collada file).
However, Pepakura (a mesh unfolding software for paper templates) primarily supports OBJ files, so I needed to convert the .DAE to a .OBJ. To do that, I used Meshlab to convert the file type. All that was needed was to open meshlab, import the dae, and export it as an obj.
The next step is to unfold the mesh in Pepakura. Since I have a mac, I used a VirtualBox Windows 10 virtual machine to run Pepakura (which is only Windows supported). I opened the obj file in Pepakura and hit the unfold button. Pepakura by default attempts the keep the object connected, but since the outside of the cube and the inside of the cube have to be different colors, they must be separated. Thus, I split the square faces from the triangle faces in a way I felt would be easy to assemble and arrange on a template. Once I was happy with the arrangement, I printed the Pepakura as a PDF using CutePDF Writer.
The final step was to make the template and duplicate each unit an appropriate amount of times. Each cubie has one piece for the outside, and 2 for the inside, and 1 bonding strip. Thus, I opened the PDF in Adobe Illustrator and made 16 copies of the inside piece on one page, and 4 duplicates of the outside square faces and bonding strips. I scaled all the parts down a bit to fit all of them on, which is why they don't match the 2 inch dimensions I made them as. After saving the new PDF, I duplicated the last page, creating a total of 8 outer pieces and strips. I added my logo and info, and I was done!
If you are interested in any of the files I mentioned above, I have attached them all below, including the SketchUp, OBJ, DAE, the Pepakura, and of course, the template. The Pepakura file is especially helpful if you are looking to scale the model up or down. You may not be able to open the SketchUp file depending on what version of SketchUp you have, so if you have compatibility issues, simply import the DAE file. You can also use 3dwarehouse.sketchup.com to convert it into whatever version you need.
Now that you know what took to design the geode cube, let's move on to actually making it.
- Cube Units .obj
- Cube Units.dae
- Geode Cube by Verticees.pdf
- Geode Cube by Verticees.pdo
Step 2: Materials
You don't need much to make this model. Here's the material list:
Template: Download the PDF template for this project below. The first page is for the inside of the cube (aka the Star), and the last two are for the outside of the cube. Please don't redistribute this file as your own.
Glue: Aleene's Quick Dry Tacky Glue has always been my go-to glue for papercraft. It bonds paper very quickly, so you can assemble faster. However, most tacky glues should work fine, and certain glue sticks will work as well.
Paper: The most important part of this model is the paper. I'm using acid and lignin free cardstock from Michaels to ensure the longevity of the model. It has a 65lb or 176g/m^2 weight. You'll only need 3 pages of cardstock: the first page needs to be one color for the inside, and the last two pages need to be a different color for the outside. Because I'm making a geode cube, I chose red for the crystal inside, and black for the outsides.
Scissors: I always use my Scotch stainless steel scissors for cutting out the pieces, but you can always use an X-Acto knife if that is your preference. Anything that can cut paper and create a clean edge will do.
Ruler and Scoring Tool: I always recommend using a ruler and scoring tool to make folding easier. I use something like a dead pen or a mechanical pencil without lead to run the point over each crease line, and the ruler helps to keep the point straight. By "engraving" each line, it makes it very easy to fold each line. I always recommend it.
Toothpicks: Toothpicks are useful if you are using a liquid glue. I use it to spread out a small amount of glue over the length of the flap, which helps prevent excess glue from spilling out and speeds up the drying process.
ALTERNATIVE - Clear Scotch Tape: The transforming star uses paper "bonding strips" to hinge each cube. However, you could easily use clear scotch tape instead. The reason I did not do this is because I have always been against using tape on the outside of paper models; I believe it takes away from the appearance and makes the product look shoddy. However, if you are fine with using tape instead of my bonding strips, please do by all means. Using bonding strips will make the model more resistant to transforming, so it will tend to stay in a cube state unless you hold it as a star. Tape however will be easier to fold and keep in a star shape.
Step 3: Printing, Cutting, Scoring, and Folding
Let's go ahead and create the pieces and prep them for assembly. The first step is to print out the PDF on cardstock. Remember, if you want a two color model, use a different color for the first page. I chose red for the inside (1st page) and black for the outside (2nd and 3rd page). Printing on black may make the ink slightly harder to see, but as shown in the pictures above, it can still be distinguished when working, especially in good light (although I apologize if any numbers or lines on the black paper do not show up in photographs). In fact, I enjoy working with black paper because it is very difficult to see any smudges from touching the paper, which makes it a good choice for using on the outside of this cube. Thus, don't be afraid to print on black paper!
Once its printed, you're ready to cut each piece out. Use the scissors to cut carefully on the solid lines, except for with the bonding strips. Only cut on the outer border of the bonding strips, since the middle solid line is the folding line.
Now, score each line using your tool and ruler. Align your ruler along each line, and run the point of the tool along the line. Apply enough pressure to make an impression, but not enough to damage the paper. Do this for every line; it may take a while, but it is a must for a good quality model. Don't forget to score the middle line of the bonding strips too!
Once you have every piece scored, sort all the pieces out. There are two types of pieces for the inside of the cube, since they face in two different directions. Sort out each piece into piles. At the end of sorting, you should have 8 of each kind of piece, for a total of 32 parts: 8 left curved inside pieces, 8 right curved inside pieces, 8 outer pieces, and 8 bonding strips. See the picture above to see all of them.
The last bit of piece preparation is folding. There are two kinds of folds, mountain folds, which crease outwards (in relation to the printed side of the paper) and valley folds, which crease inward (see the pictures above to understand the difference). In this PDF, the evenly dashed lines are valley folds, while the unevenly dashed lines are mountain folds. The scoring you just did should help make the folding process quick and easy. To see the different kinds of lines and what the pieces should look like after folding, check the pictures above.
When folding the bonding strips, I highly recommend folding it in half repeatedly in both directions, so the paper is used to bending back and forth in the final model.
At the end of folding, you should have 32 sorted, folded, ready-to-go pieces.
Now, let's move on to assembly.
Step 4: Assembling a Cubie
To begin making each cubie, start by grabbing an outer piece, and gluing the 1-1 flap/edge pair. This is all that is needed to form the outside of the cubie. Next, glue two corresponding inside pieces by joining them along the 5-5 and 9-9 edge/flap pair. Now, you will have to correctly place this inside the square cubie shell. Start by gluing on the 2-2 pair, and then attempt to glue the rest, starting with the 8-8 bond and then the 3-3 bond. You may eventually arrive at a point where there is only one edge left to glue, but cannot directly apply glue to the flap. If this happens, use the nozzle of the bottle to dispense some glue inside and spread it carefully with the toothpick (which is helpful in narrow areas). Then, squeeze the edge to finish the cubie. That is the order I chose to assemble my cubies by, but you can do whatever you find works for you.
Once you have successfully made one, repeat this process 7 more times for a total of 8 cubies.
Step 5: Understanding the Assembly
For the cube to properly unfold, each cubie and strip must be correctly positioned. To help with this, I created the above GIF to show where all the strips are located. In addition, I added screenshots of 3d models depicting how the final star will unfold. Don't worry, I'm going to cover the physical assembly in great detail in the next step.
Below is the file containing the models shown above, giving you an interactive view of how the cube should look when it is assembled and during each step of transforming. You will need Sketchup 16 or later to open the skp file, so I added the DAE file as well so you can import it into whatever version of Sketchup you have. You can also use 3dwarehouse.sketchup.com to convert the SKP into whatever version you need.
Step 6: Joining the Cubies
Joining the cubies is a very careful process. Here is how I recommend doing it:
- Start by laying out 4 cubies, correctly oriented like those in the pictures above, and glue two bonding strips on opposite sides of this layout.
- Then, lay out the 4 remaining cubies in the same formation, and flip them over to place on top of the layer you already created.
- Now, take four bonding strips and glue two on each side of the cube that does not already have the bonding strips from the first step.
- Lastly, glue the remaining two strips on the top of the cube in the opposite direction as those on the sides of the cube.
It's difficult to explain in words, but luckily, thats what pictures are for. Please use the pictures above as a more clear visual of what to do. If that is not enough, I attached a Sketchup File and DAE file showing how the finished model (with strips) should look in the previous step. You may find the photos and GIF from the previous step very helpful in completing this step. I also added a video above to show you how it should unfold (I used gloves so I didn't smudge any glue from my fingers onto the cube).
Tips on gluing the strips: When applying glue to the bonding strips, apply glue on the printed side so that the printed crease line does not appear on the finished model. Also, keep the glue about 2 millimeters away from the center crease line so two cubies don't accidentally get glued together. Lastly, always align the center crease on the strip so it is parallel with the line between two cubies, which ensures that the hinge action is straightened.
Once you've successfully glued all your strips on, your cube is done! Try folding it out and transforming it into a star to test that everything has been done correctly.
Step 7: Finish and Variants
Congrats on finishing your Geode Cube! If you make another one, here are some things you an try:
- Use special metallic, textured, or patterned paper for the inside. The more eye catching, the better!
- Use unique paper for the outside of the cube as well, so both the inside and outside are just as exciting.
- Scale the template up to make a bigger cube, or scale it down for a smaller one
- Apply magnets on the inside of the cube to make it more secured in one position.
- Make a stand for your cube so you can display it at an angle!
- Try joining two cubes together, if possible
If you have any other ideas, feel free to comment it below! Also, please share a picture if you end up making one yourself. I hope you had fun making your Geode Cube!