## Introduction: FIT to Fold

I was tidying up my room and found this pack of really nice large origami paper that I got from an OrigamiUSA convention a few years back. Why not try making something with it? The pattern is great, and I love how patterns spice up modular origami, so I decided to make Tom Hull's Five Intersecting Tetrahedra (FIT). It's a puzzle in patience and perseverance, but hopefully this Instructable can make it a bit easier!

**What you will need:**

- Paper!
- Eventually you will need 30 rectangles with a 1:3 side ratio. You can measure and cut, or start out with 10 squares and I'll show you how to find thirds from a square. I recommend 2 squares of 5 different colors. Try for something around the thickness of printer paper. Normal origami paper might be too thin to keep shape, and cardstock is too thick to fold easily.

- Some sort of cutting device, eg
- Scissors
- X-Acto Knife and cutting mat

No rulers or glue needed here for origami! The result is surprisingly stable.

## Step 1: Prepare the Paper

**OPTIONAL:** The paper I found wasn't kept totally flat and is pretty large, so I started out by ironing it flatter.

First thing to do is to prepare the paper. The model is Five Intersecting Tetrahedra, so we'll need to make 5 tetrahedra (or a triangle-base pyramid). Each pyramid has 6 sides, so 30 pieces total! I find it easiest to have each tetrahedra to be a different color, but it will also look nice as all one color.

Traditional origami typically starts with a square piece of paper, but the FIT will require 1:3 rectangles to start. But you can easily make 1:3 rectangles from squares by just making a few folds!

First we're going to fold the paper in half by matching two opposite sides together. You'll get a crease that matches the dash-dash-dash line and splits the paper in half.

Then we're going to fold the paper square along a main diagonal by matching two opposite corners together. You'll get a crease that matches the dash-dot-dash line and splits the paper in half diagonally.

With the paper split vertically, find the half that has the diagonal running through it. We're going to make the diagonal of this half. Make a crease going from the vertical middle fold to the opposite corner that intersects the main diagonal. The crease will match with the dash-dot-dot line.

The point where the two diagonal lines intersect, indicated by a star in the picture, is 1/3rd of the length away from the closest edges. You can find the proof that the star marks the 1/3rd point here.

Now take the opposite side and fold to the point and make sure the edges up. Make a nice crease and unfold. Fold the first side to the line you just made and make a nice crease. The paper should be able to fold nicely now into thirds!

## Step 2: Separate Paper

Now you have a square that have crease marks at the thirds points, and can proceed to cut the separate pieces out!

I prefer using a knife, straight edge, and cutting mat to cut the paper, but you can reinforce the folds and tear, or cut with scissors as you feel comfortable.

You measure out the width using one square and use that as a reference to cut the other squares out.

You should end up with 30 rectangles each with a 1:3 ratio.

## Step 3: Fold the Modules Part 1

Now that you have 30 1:3 rectangles to work with, you can start folding the tetrahedra pieces!

A piece of paper can have two different colors/patterns on it. I am going to refer to the side that will be showing at the end as the patterned side and the other side as the blank side.

Start with the rectangle with pattern side down.

Fold in half hot dog style (match the long edge to the long edge) with blank sides touching, and unfold.

Now fold the long sides to that middle line you just made and remember to make really nice creases. It's OK if there's some space in between the two long sides, try to minimize it but make sure they don't overlap.

You should have something that looks like this now. We're going to focus on one of the edges now, and repeat the next few steps on the other side later.

## Step 4:

Let's look at the right edge and have the rest of the piece trail out to the left. ****WARNING: You will NOT crease this next fold ** **Take the bottom of the piece and bring it to meet the middle. PINCH (not fold) so there's only a little line on the edge of the piece here. Now unfold and see something like this.

The little line on the bottom half will act as a reference point to make the next fold. The next crease will intersect with the right most mid point. Take the corner and swivel it down until it reaches the little line that you just made, kind of like you're dog earing a book page. So the point will be on the line, and the crease will reach the edge of the paper at the middle crease, like this picture. Use your fingernail to make a nice crease and unfold.

We want to make a similar fold on the bottom side, but it will line up with the crease you just made! So take the bottom right side and line it up with the crease you just made. On the bottom side we're going to take the right edge and line it up with your new crease, effectively bisecting the angle there.

## Step 5:

Almost done with this side! We want to tuck the top side into itself. Poke it through until you see a flag like this, the folds that are already there will reverse themselves and pop like magic. Tuck the ear inside, and then we can move on... To rotate the piece and do the same thing again!

Put the side you just did hanging off to the left again and repeat so you have the same thing on both sides.

WHEW!! Nice we have one down... 29 more to go! Once you've finished making them all, then you can start assembling!

## Step 6: Double Checks

Make sure the pieces have the same **chirality**. Which just means make sure they all look the same. We do NOT want them to have opposite sides tucked in, like this. So make sure to rotate the paper instead of sliding to the other side.

Do not want super overlap.

Do not want not far enough in half.

## Step 7: Make Your First Tetrahedra

The bottom piece will fit into the inverted piece like a pocket.

Bring a third piece to be pocketed by one side and pocket into the other one.

A fourth piece will connect two pieces, pocketing in one and being pocketed in the other.

A fifth piece will complete a third on one side and start a trio on the other.

A sixth piece makes the last bar to complete a tetrahedra.

To practice the assembly, you can make all 5 separately and then take them apart for final assembly, like here!

## Step 8: Weave the Rest of the Pieces

Each tetrahedra will interface with another. There are all sorts of fun symmetries with the model that you'll also find as you put it together.

Roll your shoulders, put on some relaxing music and let's get started!

Putting two pieces together is relatively straightforward. Have a single tetrahedra. Put together a corner of another tetrahedra and hook it through so that each leg is going through each face of the first tetrahedra. While it's poked through, finish the second tetrahedra, making sure the rest of the pieces do not go through the first tetrahedra.

Continue with others making sure that they all interface with each other like this.

## Discussions

Is it hard to get them all woven together like in your main image?