Flat-Foldable CP -- 3 of the few Characteristics

There are a few characteristics of a Crease Pattern which are essential to make a model flat-foldable. For this cause, I will use the CP of my panda Portrait and describe the characteristics of it. I will not go into details of why they are this way but this should serve as something educational and appreciating the nature of Origami Crease Pattern.

It is based on Mr Robert Lang's Origami design Secret book and some Youtube videos as well as books available for purchase at their respective stores like Origamics and etc.

Characteristic 1: Number of Mountain folds - Number of Valley Folds = +/- 2

Why plus or minus? That's because it is dependable on which side of the CP you are on. Logically when one side up is a mountain fold, the other side should be a valley fold. Now look at every vertices on the CP excluding the ones at the edges of the paper. I did not label the colored lines but for reference, lets assume Red line is Mountain fold and blue line is Valley Fold.

Now look at any vertices ( where 2 or more lines intersects as denoted by the black dots). Count the surrounding Mountain and Valley folds. Since this CP is completely falt-foldable, all the vertices in the center must at least exhibit these characteristics. The vertices at the edges are not necessarily true because there are folds that cannot be folded due to it being at the end of the paper.

Characteristic 2: Two Colorability

When a fully assigned CP is done with necessary folds only, one is able to color polygons in the CP such that no colored Polygon will be adjacent to each other; they will be colored alternatively. For example below, There are no Polygons that are colored touching each other!

Many Origami-Artists are doing beautiful art based on this characteristics. The magnificent part is that by folding these lines, we can get to the base of a model which is special. Think about this, this piece of art here can be used to and make out a portrait of a panda's face.

As practice,you can try to do this on a birdbase of a crane but be careful to draw lines that are used and omit unfolded lines which may be formed during the folding process!

Characteristic 3 : Alternate angles within a Vertice will form a 180 degrees angle or in short, a straight line

So for this, the characteristic would be

Angle a1 + Angle a2 = Angle b1 + Angle b2 = 180 degrees

There are mathematical proofs for this but I wont evaluate it in this post. This is indeed true if you were to inspect the vertices that are not at the edge of the paper! Explore it in the CP above!

I hope this post had allowed you to understand the nature of the crease pattern for any origami model that folds flat and continue to explore with the characteristics!

For more enquiries, you may contact me and/or leave a comment below!