3D Modeling and Printing Your Own Shadow Cube

An initials shadow cube is a cube in which each view of the cube (top, front, and side view) is the profile of a different letter. This comes from the book Gödel, Escher, Bach, by Douglas Hofstadter. A shadow cube is a really nice basic 3D design challenge, and will get you accustomed to some of the features of the 3D design program of your choice.

Making this is great practice if you're just getting into 3D modeling and 3D printing. By making one of these, you'll likely get used to some fundamental 3D design practices, and you will also be able to 3D print one to show off to your friends as a personalized keepsake!

(Also, if you were wondering, the first image is my 3D printed model suspended from strings. I edited out the strings for dramatic effect)

If you don't know anything about 3D design, check out this Instructable, which comes with a list of free 3D design programs to help you get started. If you're new to 3D design, I would suggest Tinkercad (free online intro 3D design platform) or Autodesk Fusion 360 (Cloud-based CAD platform with a lot of applications, free for students), both of which I'll be using in this walk-through. Both programs are similar to many other 3D CAD programs, so don't worry if you have another program in mind or don't like Fusion or Tinkercad. If you can't find a certain feature or tool I describe, it probably exists under a different name, so just look it up if you are unsure.

The first step is to look at the letters of your initials and figure out how complicated the geometry is, and how you should use their geometries to your advantage. Don't be afraid to take some artistic liberties in your design!

My initials are ASC. Looking at the letters, I know that I can manipulate the "A" to make it look pretty square, as well as the S. However, I know I need to pay attention to where the "cutouts" on all of the letters will go, like the right side of a "C" or the loops of the "S", because a cutout may cut through important parts of other letters. If you start out and realize that may happen, that's ok! Try re-orienting your letters to or starting on a different one.

I figure that the "C" would be a great letter to start with because it is fairly simple, yet takes up a lot of room. So here we go!

Alright. The first step in the design process is to create a cube of the size you want. In Fusion, I started a sketch and made a rectangle that was 30 mm x 30 mm, and then extruded it up by 30 mm to make a cube. In Tinkercad, I just dragged out a cube shape and scaled it up to 30 mm x 30 mm x 30 mm.

I've started with the "C", so now I need to figure out how to draw it. Note that I'm not using any of the text or letter making tools in my programs, because I want to be able to play around with my letters a bit more than that. I really like the idea of having a round "C" instead of a square one, so in Fusion I created a sketch on the top face of the cube, and I drew a few circles and lines to create the "C" shape, making sure to make it as big as possible while still staying within the limits of the cube.

As I explained previously, Tinkercad is slightly different from Fusion. Instead of starting sketches, I'm just going to drag shapes into my workspace. I probably should have started with a cylinder for the C, so I deleted the cube and placed in a "tube", because it is more fitting to the "C" shape. I then added a "roof" piece, rotated it 90 degrees and made it 30 mm tall. Tip: If you hold the "shift" key in Tinkercad, your parts will scale in all directions equally when you resize them.

To finalize my drawing of the first letter, I need to edit my shapes a little bit. In Fusion, I used the "trim" tool to cut away excess lines and curves so that all I have is the "C" shape and the outline of the box. I've also added some constraints to keep the lines where I want them.

In Tinkercad, I've adjusted the roof piece I've added to make sure the point is centered in the middle of the circle. I then selected the piece and turned it into a "hole".

Now we're ready to cut out the first letter! In Fusion, this can be done by selecting the negative space around the "C" shape and using and extrude cut to cut all the way through the cube. In Tinkercad, you simply need to "group" the hole section with the tube section, and the C will be done.

Now it's time to start on the next letter. In Fusion, you won't be able to select the curved faces (like the "C") to start a sketch, you'll need to start a new sketch on one of the origin planes. I selected the YZ plane, and now I'm ready to select the next letter.

In Tinkercad, you can drag in a new workplane if you want, but because of the curved shape of the "C", I can't create a nice perpendicular plane to work from, so I'm just going to build my next letter from the original workplane.

Now I'm starting on the "A". You'll notice I'm not doing my initials in order, because I think it's simpler to cut them out in the order that seems most convenient to you. In Fusion, you can use the "Project/Include" feature to project the shape of the previous letter onto the sketch plane. It basically turns all of the edges of the model into lines on the sketch. This can help when you're drawing the next letter. Just like I made the C, I can use the various sketch tools and constraints to create the "A" shape that I want.

In Tinkercad, I dragged some shapes out to cut out the holes for my "A". It's a bit tricky figuring out how to make certain complicated shapes sometimes, but once you play around with it enough it's fairly simple to understand how to produce the effect you want.

Just like last time, we want to cut out the negative space of the second letter. In Fusion, because I started the sketch on an origin plane, I had to cut out the sketch on both sides. In Tinkercad, I converted the two rectangular prisms I made into holes, and then I grouped all three objects.

Now you can see that the letter cube is coming together. However, because to cuts were made from two different directions, you may have accidentally taken out some material you didn't want to, and it may have messed up the profile of the first letter. If that's happened, try redoing the second letter on a different face of your model, or try rotating the letter so that the cut is the way you want it. As you can see, my models turned out fine. I can clearly see the "A" from the side view and the "C" from the top view.

Now it's time for the last letter, so start a new sketch on the other origin plane (In my case, the XY plane) in Fusion. In Tinkercad, I can create a new workplane on the face of one of the cuts that I had made from the "A" by dragging a workplane to that face. You can already see that the first two cuts have altered this face of the model slightly. Some letters will cause more damage than others, but this is really when you'll need to think about the orientation and design of the last letter.

As I just mentioned, some of the other cutouts will have affected this face of the model. But that's ok! You can use them to your advantage here, and this is really where you may have to take some artistic liberties. I've decided to construct my "S" around the notches in the sides of this model, so in Fusion I've drawn where I want to cut out material in those areas, and in Tinkercad I've made boxes of that shape to slice out the parts of my S.

Now you're almost there, using the same cut techniques I've used before, you can cut out the pieces to make the last letter. Just use an extrude cut in Fusion, or a hole and then group feature in Tinkercad.

Now is the time when viewing your model from all angles is really important, because you need to make sure that your model is still one body, and that all of your letters still look like letters. Use the viewing tools to rotate your model around and see if each profile still looks like the letter you want. If there are, you can fix them by manipulating your sketch. Try rotating one of the letters, or seeing if there is a different way you can design it to fix the problem. Some letters are definitely easier than others.

When inspecting my model, all of the faces turned out fine, except you'll see that the intersection of the bottom cutout of the "A" and the bottom section of the "S" created a free-floating feature, disconnected from the rest of the body. I'll show you how to remove this in the next step.

There are a couple different ways you can go about removing floating bodies in Fusion. I'll be using the simplest method, which just involves using the "Delete" tool. If you select the body in the Feature Tree, you can right click on the body itself and click "Delete", which will easily remove the part. You could also use the Extrude Cut tool and only cut away that section of the part if you wanted to.

Because Tinkercad is a bit more basic, the main body of the shadow cube and the small floating piece still register as the same body. To remove the small segment, I reset the workplane (by dragging the workplane tool to an empty space), and dragged and scaled a box to cover the floating section. Then it's just a matter of making the box a hole, and grouping all the components again.

After I've completed the basic design of my model, I like to add some finishing touches to it. You can modify your cube however you want at this point; you may want to fillet the edges to make it look a bit cleaner, or maybe you'd like to add a key chain or necklace loop to turn it into a personalized piece of jewelry! It's completely up to you. If you're planning on 3D printing this, you may need to adjust some of the parts of your model to avoid using support material.

If you have access to a 3D printer, this is a great item to print out as a small gift or keychain. Print it out and see how it looks! If you suspend it from threads, hang it in a corner, and cast a light on it from the top, front, and side, each of the letters will be projected onto the walls and floor. The threads in the above photo were edited out for dramatic effect. If you aren't familiar with basic 3D printing design practices, I would suggest checking this 3D printing Instructable out so learn the basics.