Origami/Techniques/Model bases

In origami, a model base is the structural skeleton of an origami model in its simplest form. The usage of a base has many benefits; the folding sequence will be easier to remember and create diagrams for, and further models can be developed from the same base, or from slight modifications thereof. However, the use of a base does, to a certain extent, limit what can be done with the model.

Traditional origami models were often developed from similar patterns. While some of them are rarely used, there are six that are used quite frequently: the waterbomb base, preliminary fold, kite base, fish base, bird base and frog base. Most recently published books only assume the knowledge of these bases; however, some authors still use unconventional bases.

These bases are referred to as the classic bases, and were used as the primary design technique until the 1960s. They all share the same symmetry, and certain structural properties. In the 1960s, paperfolders started trying to find new bases to create more complex models. One of the new techniques they developed was to fold the corners into the center (a blintz base), fold the base, and then unwrap the extra layers of paper. This technique allowed folders to multiply the number of points on the base, and is referred to as "blintzing" the base.

The windmill base, helmet base, umbrella base and pig base are found in traditional models, but not used or accepted as widely.

Models are typically classified by the number of simultaneous folds to realize. The more the number of folds is high, the more the techniques involved in the construction is complex.

Basic skills: one fold

• A valley fold is the first basic fold, in which the paper is folded in front of itself.

Valley fold

• A mountain fold is the second basic fold, in which the paper is folded behind itself. An easier way to do this is to turn the paper over first and then do a valley fold and turn the paper back over again.

Mountain fold

• The book fold is a valley fold that folds the paper by the middle and entirely covers the side up.

Book fold

• The cupboard fold is two valley folds that push the edges of the paper to the middle.

Cupboard fold

• The pleat fold is several evenly-spaced parallel mountain and valley folds. It is also called an "accordion fold."

Accordion or pleat fold

• The radial pleat fold is an angled pleat fold, usually with a focus point on an edge or corner.

• The kite base is merely two valley folds that bring two adjacent edges of the square together to lie on the square's diagonal.

Kite base

• The helmet base consists of a diagonal valley fold that bisects two corners of the square and two perpendicular valley folds that push two corners of the triangle to the third one.

Helmet base

• The blintz fold is made by folding the corners of a square into the center. This can be achieved with higher accuracy by folding and unfolding two reference creases through the center.

Blintz fold

Origamies that are done by creating only one fold at a time are called pureland origami. Because of these restrictions, proponents of the theory have devised alternate methods of folding more complicated steps that have very similar results.

Simple compound folds: two folds

Simple compound folds require simultaneous valley and mountain folds but the creases can be made before the actual folding.

• The preliminary fold or square base consists of a diagonal mountain fold that bisects two corners of the square and two perpendicular valley folds that bisect the edges of the square. The paper is then collapsed to form a square shape with four isosceles-right triangular flaps.

Preliminary fold or Square Base

• The waterbomb base consists of two perpendicular valley folds down the diagonals of the square and a mountain fold down the center of the square. This crease pattern is then compressed to form the waterbomb base, which is an isosceles-right triangle with four isosceles-right triangular flaps. The waterbomb base is an inside-out preliminary fold.

Waterbomb base

• The squash fold starts with a flap with at least two layers (for example, one flap of a waterbomb base). Make a radial fold from the closed point down the center of this flap. Open the flap and refold downward to make two adjacent flaps.

Squash fold applied to one flap of a waterbomb base

• The pig base consists of a cupboard fold with all the paper corner squash folded to the center of the paper. All the paper edge is along the middle line.

Pig base

• The umbrella base consists of a preliminary fold with all the flaps squash folded and the isosceles-right triangular flaps valley folded on the big isosceles triangle.

Umbrella base

• The windmill base consists of four preliminary folds on a single square.

Windmill base

Low-intermediate skills: three folds

Low-intermediate skills require simultaneous valley and mountain folds but not all the creases can be made before the actual folding.

• A rabbit ear fold starts with a reference crease down a diagonal. Fold two radial folds from opposite corners along the same side of the reference crease; the resulting flap should be folded downwards so that the previous edges are aligned.

Rabbit ear fold

• The fish base consists of two radial folds against a diagonal reference crease on each of two opposite corners. The flaps that result on the other two corners are carefully folded downwards in the same direction. In other words, it consists of two side-by-side rabbit ears.

Fish base

• A petal fold starts with two connected flaps, each of which has at least two layers. (For example, two flaps of a preliminary base). The two flaps are attached to each other along a reference crease. Make two radial folds from the open point, so that the open edges lie along the reference crease. Unfold these two radial folds. Make another fold across the top connecting the ends of the creases to create a triangle of creases. Unfold this fold as well. Fold one layer of the open point upward and flatten it using the existing creases. A petal fold is equivalent to two side-by-side rabbit ears, which are connected along the reference crease.

Petal fold on one half of a preliminary fold

• The bird base, or crane base, consists of a preliminary fold with both the front and the back sides petal folded upward.

• The frog base starts with a waterbomb base or preliminary fold. All four flaps are squash-folded (the result is the same in either case), and then the corners are petal folded upward.

Frog base constructed on a preliminary fold

If a square is blintz folded, then a kite/fish/bird/frog base is folded, and the blintzed edges teased out and collapsed n a certain fashion, this is called a blintzed kite/fish/bird/frog/base, which doubles the complexity and adds more points and edges to the original kite/fish/bird/frog base, for a more complex model that requires more points. It's possible to double blintz for a double blintzed kite/fish/bird/frog base if needed. Theoretically an infinite number of blintzes could be performed to yield an infinitely complex multipointed base, but paper thickness restricts this to generally two blintzes.

Mid-intermediate skills

• The Swivel fold is difficult to describe as the term is loosely defined and there are so many different versions that could be called "swivel folds". However, generally swivel folds involve a flap of paper "swivelling" at a certain point or vertex and another flap or edge of paper, connected to the first, dragged around that point or vertex.

• Pentagon. Although most origami models start with a square or rectangular sheet of paper, a few start with a triangle, pentagon, hexagon, circle, or other convex sheet of paper. A pentagon can be traced (from a template) onto a square sheet of paper, or it can be folded from a square sheet of paper. One technique for folding a pentagon uses folds to calculate the golden ratio: (1+sqrt(5))/2. Another technique for folding a pentagon uses folds to divide a 180 degree angle into five (almost exactly) equal angles. The excess paper is often trimmed, before starting to fold the desired model. Pentagons are used in five-sided flowers, such as the cherry blossom and Marie's Rose.

High-intermediate skills: four folds

• Most of the creases in a stretched bird base are present in the regular bird base. When forming this bird base, make sure to crease the triangle at the center corner through all layers. (If you unfold completely, you will see a small square at the center of the paper.) After forming the bird base, either partially unfold the paper, and/or "stretch" two opposite corners of the bird base. These two corners, their associated flaps, and the central square will all lie flat. The other two flaps will form a pyramid. Rabbit ear each flap that is in the pyramid, so that the model lies flat. All of the raw edges will lie along the centerline of the model. The stretched bird base is used in Lang's Bald Eagle, Greenberg's Eeyore, and some other high-intermediate and complex models.

• The open sink usually involves opening out the paper, and reversing creases to make a waterbomb base in the middle of the model.

• The open double sink is equivalent to making an open sink, and then open-sinking the point in the opposite direction. It is a sinked analog of the crimp fold. When made in a single step (after pre-creasing), it can be easier to make than a single open sink, because it does not require neatly reversing the point. The open double sink is used in many box-pleated models.

• The spread squash can similarly be considered the sinked analog of the squash fold. It is used to flatten a closed flap or twist fold (see below). Instead of creating a long point to one side of the flap's base, the spread squash creates a wide splat around the flap's base. The spread squash is used in the eyes of Engel's Octopus, in Marie's Rose, and in some other intermediate and complex models.

• The closed sink simultaneously makes a locking flap inside of a sink. It is difficult because the paper cannot be opened out further than a triangle. This technique is illustrated in the Origami Forum's thread #462. The closed sink appears in some high-intermediate and complex models.

• The twist fold involves, as the name implies, twisting a section of the paper with respect to its original position. The section twisted will be a polygon; the numerous required support creases include pleat folds radiating from its corners. Marie's Rose demonstrates this on a pentagon.
  • It is also possible to twist a single conical point indefinitely, collapsing the sides in a waterbomb-base-like fashion as one goes. (If this is tried with a non-conical point, such as the waterbomb base itself, eventually the fold will terminate in a spread squash.) This variant is used in many of Tomoko Fuse's modular boxes.

Complex skills

• Unsink, or sometimes open unsink, makes a concave pocket convex without fully unfolding the paper, or the opposite of an open sink. It is more difficult than the closed unsink below because there is no internal flap to grab onto to help unsink the paper, so the paper must be opened out and the area to be unsunk is pushed out (to be convex) from inside the model and from behind. It is a common fold in Lang's insects.

• The closed unsink inverts a closed sink without completely opening out the affected paper. In theory, it is "just" the opposite of a closed sink. In practice, it is very difficult, because the paper being "popped" into place usually must be pulled (not pushed), and because it involves simultaneously folding over a locking flap that is hidden inside the sink. However, it is easier to manipulate than an open unsink as there is an internal flap to pull to pop the unsink in place; in an open unsink there is nothing to hold. The closed unsink appears in some complex models, such as a few of Lang's insects.