Modular Paper Dodecahedron




Introduction: Modular Paper Dodecahedron

This is based on the work of George Hart ( But I'm not using his templates :).

It is donde with 20 equal equilateral triangles, you need at least 5 colors so you don't get two triangles with the same color together.

Step 1: Making the Triangles

So, we need 20 triangles. I used 5 square pieces of paper of different colors, I found that the configuration of the picture maximizes the size of the triangles with a side length of (square side)x((3-sqrt(3))/2). 

One way to construct the triangles is first drawing an equilateral triangle with the same side length as the square and taking the distance from the top vertex to the center of the square with a compass.

Then mark that distance from each vertex of the square to the side on its right (clockwise).

Again with the compass take the length from the other vertex to the mark you just did.

Now you have to make the triangles with the length you have with base on the sides of the square as they are on the picture.

Now you cut all the triangles :D.

Step 2: Preparing the Triangles

Now we have to make a little cut to every triangle so we can ensamble the structure later. 

I made the cut one third the side of the triangle but you can make it smaller. You ca also make them bigger but I don't know how much :P.

You can mark he thirds of the sides with a compass and then drawing the lines connecting each mark.

Now you have to cut the lines we just drew but only half of it. I drew marks on the middle of each line with not very rigorously but that wasn't a problem because the triangles were small enough. Anyway when you ensamble the triangles some times you have to cut a little more so they match.

You have to cut the halves in either clockwise or counter-clockwise orientation, otherwise you will have triangles that show the marks when you have the structure done.

Again, you have to do this with every triangle.

Step 3: Ensamble and Finish

To ensamble you have to start with 5 triangles and slide through the cuts of each of them so you get a ring of triangles.
Do this carefully, if you apply to much force, you can rip the paper and you will have to make a new triangle.
If  you find the triangles won't slide cut a little more and try again.

Now, keep on adding triangles so you continue forming these rings with pentagons in their center. Keep an eye so you don't get 2 triangles of the same color touching each other.

Finally, you get it finished :D.

I hope you like it and find it a fun as I did :).

1 Person Made This Project!


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10 years ago on Introduction

well i got every cut out and all the slits cut but now im confused on how the pattern goes all the way around. So if possible next time you create something it would be nice if you went through all the steps.


10 years ago on Step 3

I've spent almost an hour on this step (assembling 5 triangles) and am not able to get it to work. Using your first picture on this page as an example my orange and blue triangles fold flat together and my green and purple triangles almost lay completely flat with each other. Making the shape in the center a rectangle with triangle top instead of a a pentagon. I also had my bf try without any instruction from me, just showing him your instructable and having him figure it out and he ends up with the same thing. I also had him check to make sure I did everything right.

I originally only cut the slits with scissors as far as the width of the slit goes since I could always make them larger. When I ran into my problem I would cut the slits just barley wider and trying it again and again but still can't get it. This was the only issue I could think of. I might be able to go wider but I doubt it'll hold itself together without glue which wouldn't be easy to use and not have it be seen.

The only differences between mine and yours is I cut my slits on the opposite side and my triangles are a little larger. They were all carefully measured and cut.

What is it that I'm missing here? Thank you ahead of time for any advice/help you can provide :)


10 years ago on Step 3

hey there. what happens between the two last pictures? at that point there is about 10 triangles left and i am not sure how it goes. think you could add this in for clearance?


Reply 10 years ago on Introduction

I'm curious as to how this would work? I know when I built mine I needed the flexibility of the card to get the last piece in. Would definitely be impressive in sheet metal though.