Introduction: Rubik's Cube With a Twist

In this project, you will learn how to design and 3D print a fully functional, shape-shifting Rubik's Cube that solves to the shape of a twisted rectangular prism.

The official world record for solving a Rubik's Cube is less than four seconds. The industry of "speedcubing" was started by Erno Rubik, a Hungarian professor of architecture. This perplexing source of frustration that has generated about five billion dollars for the company was originally not even meant to be sold commercially. Erno Rubik created the first Rubik's Cube with no colors by hand out of wood as a teacher of three dimensional design to his students. However, he soon realized that there was so much more potential in the object than a classroom... His invention quickly rose into one of the most iconic toys of all time. Although the Rubik's Cube was at its prime in the 1980s, it left behind a new industry as its legacy, "speedcubing". Numerous companies compete with each other to design and provide the fastest and most creative puzzles that use Rubik's Cube-like mechanisms. For instance, there are types of puzzles, which use a design similar to that of a Rubik's Cube, that solve to shapes from cylinders to R2D2 from Star Wars! As clearly shown, a three dimensional turning puzzle can come in almost any shape or form. In this project, I created one that solves into the shape of a twisted rectangular prism. To see what this looks like, see the pictures above. Here is the link to the Tinkercad design:


If you want to design this puzzle, all you need is a computer and a Tinkercad account. If you would like to fabricate the design in real life, you will need a 3D printer with a potential to print at a low layer height, white 3D printer filament (preferably ABS, but mine was created using PLA and is still fully-functional), a screwdriver, and a hardware set of screws and springs, which can be acquired by taking apart a Rubik's Cube you already own or buying one from the following link: Additionally, a rasp or sandpaper and pliers are helpful. Lastly , if you would like to add color to the puzzle, you will need colored sharpies.

Step 1: Understanding the Central Mechanism

In any 3x3x3 three dimensional turning puzzle, there are four different types of pieces. At the very center of object, concealed from the outside, is the core. This core consists of six protuding tubes that points to each face on a standard cube. On the left is a picture of the core piece. The next type of piece is the centers. There six centers, which rotate, but never change on the puzzle. A screw and spring mechanism is utilized to allow the centers to be more flexible and adapt the shapes of the other pieces. The screws from the hardware set are tightly bound to the core while loosely passing through the center pieces. This allows them to rotate without loosing connection to the core piece. A spring is loaded onto each screw to allow the center to stretch away from the core slightly. This mechanism is shown in the picturte on the right.

Step 2: Understanding Edges, Corners, and Jaap's Sphere

The last two types of pieces are edges and corners. There are twelve edge pieces and eight corner pieces. These pieces move throughout the cube about the axes of the centers. Each edge has a clip that fits into the center pieces. The spring mechanism causes the center pieces to put force onto these edge clips, creating friction and thus keeping the puzzle together. This is shown in the first two pictures. Finally, the corner piece has a clip of its own that meshes with that of the edge piece, which causes the corner piece to be bound to the puzzle through a press-fit, as shown in the third picture. Although this intricate mesh explains how the puzzle remains assembled, there is still the crucial factor of turning. In a Rubik's Cube, the interior portion of the pieces, which rest on each other, form a sphere, called the Jaap's sphere. Since each clip, as referred to earlier, are portions of this common sphere, this puzzle can allow for turning on all three dimensions.The Jaap's sphere is shown in the last picture of a disassembled Rubik's Cube. This is a tricky concept to grasp, but going through the design process will help you understand it more.

Step 3: ...with a Twist!

The last concept of the design you will need to grasp is that although the interior design remains relatively constant among 3x3x3 puzzles, the exterior design can be altered vastly. Changing the outside shape of the standard cube changes the exterior of each piece to be portions of the total shape. For example, view the picture on the left to see how the exterior design is altered from the standard cube in this particular case. Changing the exterior shape usually results in there being subgroups within each type of piece, meaning that all of the edge pieces will not be identical. Since, the "twisted polygon" shape that makes up the exterior of the puzzle is relatively symmetrical and geometric, the only oddities are that there are two types of edge pieces and two types of center pieces. Changing the outer shape of this type of puzzle also implements an extra challenge for solving it; when scrambled, these weirdly shaped puzzles change shape and color chaotically, as shown in the picture on the right.

Step 4: Setting Up Exterior Cutting Planes

First, find the twisted polygon shape under shape generators, all, page 7. Drag it onto the build plate, then change the "#ofPoints" to 4, and finally set the size to 55.5 millimeters in height, length, and width. Next, take a sphere-shaped hole onto the plane and scale it to 38 millimeters in all dimensions. Center align the two shapes on all three parameters and then group them. After that, grab a box and make it a hole. Set the dimensions to 0.25 millimeters (from left to right from your viewing angle) by 100 millimeters by 100 millimeters. Duplicate this shape and move it exactly 18.75 millimeters to the right, making sure that the shapes stay aligned on the other dimensions. Each of these shapes is called a cutting plane because it divides a bigger shape into smaller pieces. Group these two cutting planes and then duplicate the grouped shape. Rotate the new body by 90 degrees (clockwise from your viewing angle). Duplicate the grouped selection again and rotate it clockwise (facing the top of the design). If you did this correctly, your cutting planes will form the axes of a Rubik's Cube (see the second picture). Then group the cutting planes into one body and center align it with the other body (which consists of the twisted polygon and the sphere-shaped hole). Duplicate the cutting planes and drag one of the cutting plane bodies off to the side. Group everything else in the design. If you did everything correctly, your design will look like the third picture.

Step 5: Setting Up Interior Cutting Planes

Now, take the extra set of cutting planes and ungroup them. Then, move each one 7 millimeters towards the middle so that the distance between parallel cutting planes is a total of 14 millimeters less than it used to be. To see the process view the first picture. Then group the six cutting planes together. After that, drag a sphere into the picture and scale it to 37.5 millimeters in all directions. Create another sphere (hole) that is 33.5 millimeters in diameter. Center align the grouped cutting planes with the both spheres and group the three shapes, as shown in the second picture (you can not see the smaller sphere-shaped hole because it is inside). Finally for this step, center align the two bodies in the design in every direction.

Step 6: Cutting Out the Edge Pieces

To begin this step, duplicate the two shapes in the design and move them together off to the side. Then take the original set of bodies and hide the sphere on the inside of the twisted polygon using the light bulb icon. Then zoom out and ungroup the twisted polygon. Next, ungroup the cutting planes as much as possible. Extend the cutting plane on the right side; change the width from 0.25 millimeters to 100 millimeters in the outword direction. Do the same to the cutting plane on the right. Then, select the cutting plane that runs horizontally and is on top and change the height from the bottom to 100 millimeters. Finally, face the design from the top and click on the cutting plane that runs right to left from the top view and is closest to the cutting planes that were already extended. Change the width of 0.25 millimeters to 100 millimeters in the opposite direction. To visualize this, view the first two images. Additionally, group all of the extended cutting planes with the twisted polygon. What's left of the shape should match the third picture. After you have confirmed that you did this process accurately, show the sphere shape and then hide the portion of the twisted polygon. Ungroup the sphere once and then the cutting planes as much as possible. Select the cutting planes of the sphere near the hidden edge piece and repeat the same process with these cutting planes, the sphere a substitute for the twisted polygon. This is shown in the fourth picture. Group all of the shapes shown in that image. Click the "show" button and group the two shapes, forming the first edge, as shown in the fifth picture. To form the next edge piece, duplicate the first edge shape you created. Then, hide everything except the new shape. Ungroup once this new shape and hide the partial sphere shape. After that, ungroup completely the body still still shown. Your shape should now look like the first picture again. Then, rotate the twisted polygon shape 90 degrees counterclockwise from the view of the first image. Then group the shapes and show the hidden bodies. Then group the new edge, which should look like the sixth picture. If you have made it this far, great job! You have gotten through the hardest part already!

Step 7: Cutting Out the Corner Piece

Now take the two shapes you duplicated and put off to the side in the last step, shown in the first picture (the outer twisted polygon shape is transparent in the picture). Duplicate the shapes and again put them off the side. Then hide all of the shapes except for one twisted polygon and ungroup it as much as possible. Then extend each of the cutting planes to 100 millimeters, just like you did for each of the edge pieces, to leave the shape of a corner, as shown in the second picture. Then group the twisted polygon with the cutting planes. Make sure not to group it with the hole shaped sphere. Repeat this same process with the sphere shape, which should look like the third image. group the shapes to match the fourth image. This is the corner piece.

Step 8: Creating the Center Pieces

To start the first center piece, create a cube that has 18.5 millimeters side lengths. Then create a sphere shaped hole with a diameter of 38 millimeters. Lift it off of the ground by 8.75 millimeters and then center align the two shapes on the x and y axis. Next, create a cyllinder shaped hole with a diameter that is at least 1 millimeter larger than the screw head you are using. Make it 8 millimeters in height. Center align the three shapes, so that it looks like the first picture. Group these shapes. After that, create a new cylinder shaped hole with a diameter 1 millimeter larger than the shaft of the screw. Extend the height of the cylinder to 100 millimeters in height. Center align the two remaining shapes and group them to finish the first center piece, which is shown in the second and third pictures (the center piece in the third picture is transparent). To create the next center piece, take the twisted polygon that you put off to the side in the last step, ungroup it as much as possible, and extend the cutting planes, as presented in the fourth picture. Group the twisted polygon with the cutting planes and sphere shaped hole. The result should match the fifth picture. Duplicate the finished first center piece you created and align it with the other shape (dark blue in the pictures) so that the curved edges are at the same place. Then, ungroup the center piece as much as possible. Delete the sphere shape and the cube shape. Then group the remaining shapes to form a body that resembles the sixth picture (front) and seventh picture (back). One more piece left!

Step 9: Create the Core Piece

To make the core piece create a cylinder that is 23.5 millimeters in height and 4 millimeters in diameter. Duplicate this shape twice and rotate each one to point to each face on the cube as shown in the first picture. Then, make a new cylinder shaped hole that is 23.5 millimeters in height and has the same diameter as the screw's shaft that you are using. Then create thin boxes rotated 45 degrees to increase strength. This is very important if you are going to 3D print this piece in real life. Group the shapes to finish the core piece.

Step 10: Adding Metafillets to Contact Surfaces (Optional)

Fillets are shapes that can be used to round out sharp edges. In this mechanism, fillets help to allow the puzzle to turn more easily. The metafillet shape is on page 12 of "shape generators". Scale them correctly so that they still leave a flat surface on each piece. Making the fillets larger could the risk the puzzle not fitting together properly. Making the fillets to small is more conservative, but will have less positive effect on the puzzle. For the corner piece, it is important to group the partial sphere with its fillets and the partial twisted polygon with its fillets first and then grouping the results together rather than grouping all six shapes simultaneously. The bottom picture shows the fillets for the interior parts of the puzzle. (The exterior parts are hidden.) The top picture shows the fillets for the exterior parts of the puzzle. Add them to the design on the surfaces shown in each picture.

Step 11: Duplicate the Pieces

In this step, duplicate each type of piece to following amounts:

The number in parentheses corresponds with the first picture and the number after the colon is the number of pieces needed.

First type of center (1): 2

Second type of center (2): 4

First type of edge (3): 8

Corner (4): 8

Second type of edge (5): 4

Core (6): 1

Congratulations, you have finished the design!

Step 12: 3D Print and Sand the Pieces

Depending on the attributes of your 3D printer, adjust the settings to print each piece. You will most likely have to print each piece individually or in batches of two or four depending on each piece. For the best results, print in the lowest layer height that your 3D printer allows and file or sand down the pieces' interior surfaces to make the components even smoother. The more time you take sanding, the smoother your puzzle will function. When I did this project, my 3D printer was having a problem with printing small details on the first layer of the prints, so the core piece I printed wouldn't form properly. I worked around this problem by substituting it with a core piece from a Rubik's Cube I disassembled. However, depending on the 3D printer to which you have access, it is definitely possible to print a functional core piece.

Step 13: Assemble the Pieces

First, each spring onto each screw. Then apply pressure while using a screw driver to connect each of the six center pieces to each hole of the core piece, so that your parts match the first picture. Then, assemble each of edges onto their respective places on the puzzle except for one of them. Each one belongs between their two respective centers, which can be determined by referring to the design; also make sure the centers are rotated correctly. You may have to adjust the tightness of your screws to adjust to the assembly process. Next, push in all of the corners into their places so that the only missing piece is one edge. Finally, slide in the last edge and enjoy your puzzle. The more you turn it, the smoother it will become.

Step 14: Add Colors (optional)

Finally, to give the puzzle an extra challenge, you can use sharpies color each side. Thank you for viewing this Instructable and hopefully it was helpful to you. Hopefully, this project will inspire you to make your own customized shape-shifting puzzles! I would greatly appreciate it if you would please vote for my project to win this contest.

Tinkercad Student Design Contest

Second Prize in the
Tinkercad Student Design Contest