## Introduction: Platonic Solid From Modular Origami

Modular origami is one of a category of origami. Make small pieces from Origami, and assemble them to complex structure. The units used in this project are square and can be combined alternately. You can make a cube by using 6 units. When 12, 30 or more units are used, the shape becomes more like a sphere, and in Japan it is called “Kusudama” and is used for decoration.

The polyhedron known as Platonic solid is composed of equilateral triangles, squares, and pentagons. On the other hand Origami is usually square, so it is not impossible but difficult to make equilateral triangles and pentagons.The shape of “Kusudama” is a star-shaped polyhedron. I tried to find Platonic solid in “Kusudama” structure. I think it's good to understand the nature of polyhedra.

In the end, I made 90 units “Kusudama”. I knew it was possible, but it was the first time I actually made it. It was so hard for me to make, because It will naturally collapse from the middle of making. If you try to make the same thing, I recommend that you make one by one by bonding.

If you are interested, you can search for "Kusudama" or "くす玉" and find something better made. There are various types of units, but regularity is often similar, so it's fun to imagine how they are made.

Anyway, 12 or 30 units are not so difficult to make, feel free to try them out.

## Supplies

Lots of origami. I used 7.5cm square paper.

## Step 1: How to Make Modular Origami Unit

At first, make modular unit from square paper. Make paper of the same size. Be careful not to get a mirrored shape.

Smaller units are easier to assemble. 5cm square or 7.5cm square origami is recommended.

## Step 2: Tetrahedron

Make cube from 6 units. You may see just a triangle on the cube, that's right. But when you connect the diagonal, it is actually a Tetrahedron.

## Step 3: Cube

It is easy to make cube from 6 units. But to unify the length of the side, I made a cube with 12 units.

## Step 4: Octahedron

Make Octahedron from 12 units. If you ignore the protruding triangular pyramid, you will see Octahedron.

## Step 5: Icosahedron

Make Icosahedron from 30 units. It seems to have suddenly become complicated, but this is the most recommended if you try to make. Assemble five triangular pyramids on one vertex.

## Step 6: Dodecahedron

Finally. Make Dodecahedron with 90 units. Why so many units?

5 triangular pyramids to make a pentagon. 1 triangular pyramid is made from 3 triangles. 2 triangles from 1 unit. Dodecahedron has 12 pentagons, so 12 * 5 * 3/2 = 90.

Participated in the

Made with Math Contest

## Comments