![]() ![]() For the regular hexagon, these triangles are equilateral triangles. If you don't remember the formula, you can always think about the 6-sided polygon as a collection of 6 triangles. Alternatively, one can also think about the apothem as the distance between the center, and any side of the hexagon since the Euclidean distance is defined using a perpendicular line. You can view it as the height of the equilateral triangle formed by taking one side and two radii of the hexagon (each of the colored areas in the image above). Just as a reminder, the apothem is the distance between the midpoint of any side and the center. The formula for the area of a polygon is always the same no matter how many sides it has as long as it is a regular polygon: For those who want to know how to do this by hand, we will explain how to find the area of a regular hexagon with and without the hexagon area formula. The easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. Funds from these links go towards supporting this site.We will now take a look at how to find the area of a hexagon using different tricks. As an Amazon Associate I earn from qualifying purchases. If you’d like to support the site, you can use the Amazon affiliate links below. If you want to print out the individual faces, you can check out the STL on thingiverse. I can’t wait to reapply these techniques towards some more creative ideas. This one will remain unfinished, but future builds could easily include some filler putty before paint. I’m very happy with it, but for any future applications I need to be more precise during the glue up, as I ended up with a few gaps and a bit of misalignment. Once these were dry, I started combining them until I had the final product. I repeated this glue up for 9 pairs of faces, leaving 2 pieces free for final assembly. If you’re looking for a faster cure, you could easily get away with cyanoacrylate if you’re confident in your initial placement. I mentioned before, but I used a multi-surface glue to give me some more work time, but I also found that it’s thickness helped fill the gaps nicely. Next, I applied a liberal amount of glue to one of the edges and folded the faces together. I decided against taping the entire length of the edges to be combined because I wanted to be able to see how the faces were coming together. This helped keep everything aligned, while still allowing a sort of hinged movement. I applied some blue tape to pairs of faces to help hold them together. I did this step in a few phases to make it a bit more manageable. AssemblyĪfter printing out 20 of these, the next step is assembly. This improved print times, and saved on filament. Lastly, before exporting to print, I made a smaller triangle and extruded it to remove a bunch of the center mass. I went with 5mm, which gave me plenty of surface area. The depth of the extrusion is a another inconsequential choice. During the operation, we’re going to specify the angle we calculated as a taper which will be applied to each resulting face. Next we’re going to apply that math we did a little bit ago. You can do this part manually, or use constraints in the application to enforce them. The important part is that we use a 60° for each corner. For this proof of concept, I used a length of 50mm for each side as they’re fairly small, but will still be large enough to work with. ![]() We don’t particularly care about the length of each side, as long as it will fit on your print bed. Modellingįirst step is to create a drawing of an equilateral triangle. Now that we have the math worked out, we can head over to Fusion 360. But, since we have two objects meeting to make up that angle, we divide by 2 or a total of -20.905°. This means our tapers need to add up to -41.81°. To get our angle, we just need to do 138.19 – 180. For a d20, or regular icosahedron, the angle is about 138.19°. From there, we can manipulate that to find the taper of each piece to have our planes form that angle. This is basically the interior angle between two intersecting faces of the die. After some searching, I discovered the angle that I needed is called the dihedral angle. The first step was to figure out how to make individual triangles fit together correctly. I avoided CA glue because I wanted something to cure a bit slower, so I’d have some time for adjusting the placement. For this project, we’ll be using a 3D printer, blue tape, and some multi-surface glue. Figuring out the math to make this work wasn’t too difficult, but this build was really about figuring out the process so I can reuse the techniques in more creative ways later. This project was a bit of an experiment to start off. Today we’re building a big d20 out of individual triangles. ![]()
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