Wide Flaps

If you know how flaps work, you know that after packing in one circle, the resulting flap is always one or two units in width. However, what if you wanted to create a flap that is more than two units wide? What would you do? This is where wide flaps come in to play. By stretching circles either horizontally or vertically, it is possible to create wider flaps.

Implementation

In order to implement a wide flap into your model, you first have to take account for two values: the length of the flap and the width/height of the flap. Normally, you would only change the flap length and keep the width at 1 or 2, but in this case, you can change each value to whatever value you want. If you wanted to make a 4 unit wide flap that is 4 units long, it would look like this:

You might have noticed that the circle shape is distorted, as the added space for the width of the circle filled up the middle. The flap width is shown in yellow, while the flap lengths are shown in pink. Now, remember circle packing? Circle packing rules apply here as well. The circle must not overlap other circles, and its center (flap tip) must not leave the paper. However, since the circle is now widened, where would the flap tip be? Well, the flap tip will actually be situated in the same place as before, but a widened flap would have two flap tips instead of one. In the example below, the flap tips are shown as dots.

According to the circle packing rules, neither of the flap tips can leave the paper, and can only exist on the paper or on the edges. However, in reality, it doesn't matter if one of the flap tips leave the paper. If this happens, it actually just changes the width of the flap itself. However, to avoid confusion, it is best to just follow these rules.

Now that you know how to pack this type of flap with the other circles, you're probably wondering how crease lines work with these flaps. Here's how you add crease lines to a wide flap: The diagonal creases, also known as axial creases, will stay the same. Crease lines will run through them as they will with a generic flap. Then, the blank space in between will be filled in with an accordian-styled columns of straight crease lines. In a model, it should look like this:

Flap Height

Also, you can change the flap height. Flap height and flap width are basically the same thing. In order to change flap height, just follow the same steps shown, but vertically. The flap tips should both be on the same column. The crease lines would also run through the same way as the horizontal width flaps. Here's an example: