Laser Cut Paper Icosahedron/20 Sided Die

For this project I made a 20 sided die inspired by my table top gaming hobby which uses this kind of die most commonly. Structural Packaging by Paul Jackson was helpful in my pre-planning and prototyping process, as I used his idea of taping a form together both to determine where I needed tabs as well as to determine the order and orientation of the numbers on each of the faces. Due to the relative simplicity of the icosahedron net, I didn’t necessarily need to mark the sides and faces in the way Jackson recommends doing, but I was able to annotate the proto-form by using an actual D20 as a reference. Ultimately this saved me a lot of time in trying to figure out where each number went, and also saved me from worrying that a wrong number would result in it not being a true D20 due to the die’s design which ensures a statistical variation in rolls, which I felt was important to keep in my recreation of the from.

-Card stock

-multi-purpose liquid craft glue (Original Tacky Glue)

-Epilog Fusion Maker 36 Laser Cutter

-Fusion 360 + Adobe Illustrator

First Ideas

For this project I explored several possible forms including a small model of Storke Tower, a spinning top, and an inversible form. Ultimately all these options were either too primitive or two complicated. Eventually I landed on geometric forms I interact with often and decided to create a 20 sided die because it is among the more iconic table top game dice.

Planning

I knew the digital design would be simple enough because of how repetitive the pattern for an icosahedron is, so I decided to start my planning for the number designs that would be on the different faces. A true D20 has a very specific order and placement for the numbers that allows for a fair deviation of rolls and I decided that I'd replicate that for my form.

First Prototype

For my first attempt I used the logic that because each number has its "opposite" on the opposite face (the opposite face of the 20 has a 1 and so on...) and created a pattern that would have the 1 and the 20 as far form each other as possible. Unfortunately this resulted in the net appearing to have the 1 and the 20 on opposite sides but when the prototype paper form came together the 1 and the 20 were actually right next to each other.

During this step I also took time to determine how big I'd be able to make my form if the net needed to fit on a 11x8.5in sheet of card stock. I decided that the equilateral triangles that make up the faces of the 3D form would be 1.85in so that the net would be just over 10in wide.

Corrected Prototype

Eventually using the same form, I taped a low quality version together and used a real D20 to write the correct number and orientation of each number on each face in green marker (I forgot to take a picture of this step). I then removed the tape so I had a net with all the numbers on the right face and in the right orientation. This step was also a good opportunity to determine whether my original sketch had enough tabs, and I determined that I definitely did not.

Parameters

For the digital design aspect I used the repetitive pattern of an icosahedron to reduce the amount of work I had to do. I first defined parameters for every line I'd use in my net including the sides of the triangles, and both lines that made up the tabs (I did not know at the time that I could define parameters for angles, though this did not impact my design).

Design

Using these parameters I made one triangle that I built the rest of the triangles around, ensuring that they all connected. I did not find that I needed to use constraints because there were no irregularities in the ways the shapes connected with each other.

For the tabs I decided that because I planned on adding numbers* to each face of the form, that interlocking tabs would be too aggressive when putting the form together and I didn't want to risk ripping the numbers so I committed to using glue and simpler tabs.

*I also decided that because each number has to be in a specific orientation that the native type tool in Fusion would be very difficult to use, and would also not translate onto my dxf file anyway so I resolved to type the numbers in Adobe Illustrator where I'd have to recreate most of my lines anyway.

Illustrator Design for Laser Cutting

After exporting from Fusion as a dxf file I opened it in Illustrator to add my numbered faces. I chose to use a stencil style font (Stencil by Adobe Originals) for the numbers because this font has built-in bridges that mimic physical lettering stencils so closed characters wouldn't just be holes that lost their defining characteristics. Once I was happy with the design, at the recommendation of the lovely Makerspace staff, I selected all my lines and set them to a stroke width of 0.001mm and saved my file for laser cutting.

Laser Cut Settings

For the settings I used the native card stock cut settings, and for the scoring I used the same settings but adjusted the power to 15% and the speed to 100%(unfortunately I did not take a picture of this screen so there is a slight chance the latter number is unaccurate). My first cut did not go well, I did not properly center the design, and before I reached the above conclusion the score was slightly too weak.

After properly centering and focusing my paper my second attempt went a lot better and many of the number pieces fell through the holes.

Before gluing the form together, I creased the scoring lines and held it together with my hands to ensure the fit was good. (As is visible in the picture below I also cut a back up because I knew that due to a scheduling conflict I would not be able to return to the makerspace before this project was due) Ultimately I was happy with the fit and planned on finishing the construction at home.

Glue

Unfortunately the glue sticks at the makerspace did not work for the form's small tabs, but luckily I was able to use some multi-purpose craft glue I had on hand and allowed sections of the form to dry in place so the tabs didn't pull on the backs of the shape's faces causing unclean edges. The whole process of gluing and allowing time to dry between sections took about and hour and a half.

Final Forms

Below are pictures of both sides of my final form and both sides of two actual D20s.

Final Thoughts

Ultimately I am very happy with my forms, looking back there are many things I would have done differently. The tabs for example at times were visible through the number hole, which did not get in the way of the number but did take from the form's clean edges. I also made a mistake and the 18s on the forms are upside-down, in a future iteration I might make sure that in my documentation I make it clear which side is the bottom for characters with vertical symmetry. In table top gaming players often have special dice that they consider lucky or important for some reason or another that they use in rolls that are particularly high stakes, I think this form could be a fun inclusion in a table top game in this way.