Pi Coin (Origami)

Hi, I'm David Tapias, I'm an origami folder and creator.

When I saw this challenge, I started thinking of ideas like creating a model that starts with a circle, or maybe something modular using circular shapes. But then I remembered a new and interesting technique that has emerged in recent years for designing origami models. The idea is to play with the two colors of the bicolor papers in 2D, almost like “painting”, the contour of each model are geometric shapes such as hexagon or octagon, which can near to the circle shape. That’s why the technique has been named Origami Coins or Pictoric Origami.

So, I thought, folding an octagon with the Pi symbol inside could be a great idea, especially because the octagon also has historical ties to the calculation of Pi, as used by Archimedes.

The origamist who introduced this technique was the Chinese artist Simple Origami (@simpleorigami094). While exploring some of his models, I noticed they often share a base. I used that base and began folding and folding, trying to create the symbol for Pi and here I will teach you my result.

Supplies

1. 1 square bicolor paper (20cm x 20cm)
2. Glue Stick (optional)

Step 1: Before to Start

In origami, there are two basic folds, and these folds are the foundation for making any origami model. The first fold is called the valley fold, and it is represented by blue lines (like rivers). The second fold is called the mountain fold, and it is represented by red dots and lines (like lava from a volcano). Check the image.

In some steps, I will talk to you about these folds, and some photos will include these lines.

Step 2: Choose the Colors

I will use a square with colors orange and yellow, and the background will be orange and the symbol of pi will be yellow.

Step 3: The Color for Pi , Up

Step 4: Halves and Diagonals

Fold as shown (those folds are Valley folds)

Step 5: Kite Base

When you fold two sides to the diagonal crease, you are folding a typical base in origami, the kite base.

Step 6: Repeat Kite Base

Repeat the kite base using the three missing corners.

Step 7: Turn Over

Turn over and identify the octagon, mark the octagon as shown.

Step 8: Turn Over Again

Turn over and make the valleys fold as shown. After the paper will start to close counterclockwise. Close the figure as shown on the last image. (That is the figure base that I told you on the introduction).

Step 9: Clockwise

Unfold to fold all tips as clockwise. We have four long tips and four short tips.

Step 10: Long Tip and Short Tip

Fold the long tip and short tip as shown.

Step 11: Squash Fold

Fold the long tip as shown. About origami, this type of fold is called, squash fold.

Step 12: Changing Folds

In this step, you must change the crease existing as mountain fold to valley fold, and the valley fold to a mountain fold on two sides.

Step 13: Hiding a Long Tip

Open all tips to hide the long tip that we are working, hide until background.

Step 14: Position

Important: This is our reference position for folding the model. So, if you need to rotate it to make a fold, once you're done, always return to this original position. The tip of the long flap that we hid should always be pointing upward.

Step 15: Lower Two Long Tips

Lower the two long tips as shown.

Step 16: Lower the Short Tip

Lower the short tips as shown, you should have the two short tips at the bottom. Move the long tip to the rigth.

Step 17: The Trick to Get the Main Reference

Open the layer as shown to fold horizzontally, the point of reference to stopt to folding will be the color change when you are folding up. The sides of the paper will lif up, flatten as shown.

Step 18: Unfold Up to Step 17

Unfold up to step 17, fold the long tip to the left and repeat the step17.

Step 19: Push the Long Tip

Using the existing creases, the paper will have tension on the long tip. Push the long tip to reverse that point, as shown.

Step 20: Fold and Unfold

Fold and unfold as shown.

Step 21: The Main Reference Again

Open the layer and fold as shown, remember, the main reference to fold is the color change. Flatten the tip as shown.

Step 22: Repeat on the Other Side

Repeat the step 21 on the other side. Unfold to where shown.

Step 23: Outside Reverse Fold

Now, you must making an outside reverse fold with the orange triangle, we have all creases, so the paper should pull towards those folds. Open the layers as shown to make most easy the folds and avoid breaking the paper.

Step 24: Valley Fold

Open the layer and making the valley fold as shown. Unfold.

Step 25: Repeat As the Step 19

Using the existing creases, the paper will have tension on the long tip. Push the long tip to reverse that point, as shown. The yellow color on the little triangle, it will must hidden fully.

Step 26: Repeat on the Other Side

Repeat on the other side the steps 20 to 25.

Step 27: Hide the Short Tip

Using the existing creases, fold the short tip as shown, After, inside reverse fold to hide.

Step 28: Trap the Layer

Fold the long tip to the left, open the layer and you can see a triangle, fold the triangle to trap the layer as shown

Step 29: Rabbit Ear Fold

Fold as shown, The image 6 is showing a rrabbit ear fold but on mountain fold. The size of the left long tip is a little bit major, so you should making a little fold to adjust that. The little extra mountain fold is shown inside the circle.

Step 30: "Foot Right"

Fold as shown, the fold has not reference. After, unfold.

Step 31: Use the Refeference and Fold Again

Using the references to the last folds, fold a valley fold, after using the existing creases fold again as shown.

Step 32: "Foot Left"

Fold the valley fold having as a reference the base the "Foot right"

Step 33: Trap the "foot Left"

Valley fold, note that the crease underneath starts at the tip of the triangle. Now you have a little triangle that is visible to the front. Use that triangle to trap the "foot left" insert them in the pocket as shown.

Step 34: Hide the Tip

Mountain fold to hide the tip as shown.

Step 35: Trap the "foot Right"

Repeat as the step 33.

Step 36: Pi Coin Finished

You’ve finished the Pi coin, but maybe you used traditional paper and noticed the figure opening up.

This happens because this type of origami builds up front layers.

In the world of origami, we use many types of paper, and for this kind of model, it’s always recommended to use sandwich paper.

To make sandwich paper, we use: thin paper + aluminum foil + thin paper.

If you want to learn how to make this type of paper, you can visit my website ( click here ) I have a tutorial for it.

The second image shows a Pi coin made with sandwich paper (12cm x 12cm). The figure uses no glue, and the result is perfect.

Step 37: Glue or Not Glue

One rule for considering a figure as true origami is the fact that no glue is used in its creation.

However, there are cases where the paper design may be perfect in terms of color or texture, but its thickness is not ideal causing the figure to open up easily.

This stage is considered the finalization or finishing of the model, and in such cases, there’s no choice but to use glue.

If that’s your situation after completing the model, use a glue stick, as it doesn’t add much moisture.

Apply glue as shown.

Step 38: Pi Coin Completed

Congrats !!! You completed the model.

If you want know more about origami, you can visit my web page (click here).

Thanks for fold :) .