Extra Steps

After packing the circles, there are extra steps you need to follow in order to finish the crease pattern. It follows two steps: 1, surround the circles that you packed with squares, in such a way that they fit snugly around the circle. 2, draw an "X" in the middle of the circle, with the four lines of the X extending to each corner of the square. Although these two steps might seem random and confusing, they are extremely important. Let me show you a few examples.

In the example shown on the left, you can see the three steps to create a flap on a sheet of paper. First, draw a circle. Second, fit a square around the circle. And third, put an "X" over it. This will create a flap.

In the next example, it will show a model example of how to pack four flaps into a sheet of paper. In the example, you can see four flaps, each packed on a corner of the paper. If you look closely enough at the paper, you might actually see a vague resemblence of a triangle base. That is because the model example is just four flaps packed onto a 2x2 grid. After cutting off the excess, such as the circles and the lines outside of the paper, you can see that it forms the crease pattern of a triangle base.

This example shows a simple way of designing a model, from start to end. However, since it uses a 2x2 grid, each flap only takes up one unit, or one square on the grid. In other models, one flap will usually take up more than just one unit. In those cases, you will need to draw crease lines on the flaps. Although this probably does not make much sense in written text, it will hopefully make sense after I show you an example. Before you look at the example, know that every time a crease line comes in contact with a diagonal line, it must make a 90 degree turn. Let's see an example of how this works on a corner flap.

Crease Lines

As you can see, the crease lines come in on the left side and bottom side of the paper. It may seem confusing on which sides should have crease lines and what direction they are supposed to go, so in the next example, you will see where the crease lines are placed in a complete circle flap.

The example shown above shows the process of designing a model with one flap in the center from start to finish. The first image is a blank square. Then, a circle (flap) is packed in the middle. It is not larger than the paper, its center is on the paper, and it is not overlapping any other circles, therefore, it is a valid circle. Next, the extra steps are done. The diagonal crease lines are drawn onto the circle. Next, in the second to last image, both the circle and square surrounding the circle are removed, as the only necessary element of the flap is the diagonal crease line. Next, you can see that the flap's crease lines are put in. The flaps begin at the edge of the flap and then move towards the flap tip (flap tip is the center of the circle). Then, once the crease line touches a diagonal crease, it turns in the direction away from the flap tip.

Recap

We covered a lot in this section, so as a recap, after packing circles, you have to surround them with squares, put an X inside the square, and then erase the unnecessary parts. Unnecessary parts include the circle and the square. Crease lines are lines based on the grid size of a paper. They run along the grid lines and make a 90 degree turn every time they come across a diagonal line. The diagonal lines are from the X drawn in previous steps.