Paper folding and design

On foldings

Featheriness of paper: Accidentally found free structure for making feathers.

I will go from the basis of Japanese origami folding toward the plastic experiments of Bauhaus and the basic foldings of packaging design. I will tell about a few basic foldings and a folding principle I have learned. As illustrations, I will show some blank drawings I have done during various periods for my lectures.

As a student, I made a plastic practise exercise from paper, in which an interpretive animal-themed relief had to be produced from white paper on top of a cardboard back plate. A relief, in which tridimensionality is presented as if flattened, as in medal art. Right away I had problems imitating on paper the feel, hairiness, leatheriness or featheriness of some material, but then I started to perform material experiments by tearing, cutting and pressing paper on different platforms and with different tools. I found featherniness by pressing strokes on paper on a soft platform. I did not have to choose the topic anymore, because the technique already limited the topic to birds.

Geometric folding and origami

Every free soul certainly must want to use paper for his or her own goals and purposes. Still, there are some expression techniques and material characteristics that can be more useful than others. If one wants to try geometric folding and start quickly, one does not need to fuss right away with t-squares, millimetre-precise performance numbers etc. dimensionings. A sheet of paper, a table and capable hands suffice, as in Japanese origami.

In general, one does not have to be alarmed if one does not create a unique or recognisable result right away. It is more important that one learns, for example, how to make a corner turn in an accordion folding etc. Every experiment usually produces a set of new questions/possibilities about shape and structure and thus forces one to continue onwards

One basic paper structure and how it is folded..
Folding instructions for square structure. Be carefully that you do straight and diagonal foldings from opposite sides.
All these three different shapes have a same net construction. So when you change the folding direction it forces the construction and then it makes the difference.

A common A4 sheet of paper can be folded by halving the sheet’s square into a diagonal, first in one and then in the other direction. Then the sheet is folded in a vertical direction, i.e. as halves in a vertical, and both sides still further as halves. Then the same is done horizontally by first halving the square and continuing until the whole paper is divided into a network of vertical and horizontal squares.

Then the sheet is turned around, and the folding is continued by doing the oblique i.e. diagonal foldings and utilising the already folded square foldings and sheet proportions. Thus, the oblique foldings are done from a different side of the sheet than the vertical and horizontal foldings. In this way, we achieve a sort of an “accordion structure,” from which varying surface structures are created. The folding takes place back and forth, in other words “the outward and inward folding” always follow each other in the structure.

Folding a sheet by halving it is easy. A folded geometric network forms 45-degree and 90-degree angles. Origami experts create, for example, 30/60/72 and 120-degree regular triangular networks only by measuring and folding with a sheet, and it is not difficult, only more complex. Various structures can quickly be folded from a sheet, depending on which side the foldings are done from. European artists have studied and taught the use of paper as a plastic material and flexible surface structures since the plastic design courses of the Bauhaus design school.

An image of surface structures and their folding methods in structural packaging design assignments.

When a network formed of rectangular or oblique squares is folded, we can notice that the direction/order of the foldings carefully determines the kinds of shapes created from a sheet of paper at each time, thus the same structure or network of foldings forms many different shapes.

In this image example, three completely different sized shapes that are visually different have the same structure and surface area. The direction of the foldings, however, varies, inwards and outwards in turns.

The simple wave structure idea has been used in e.g. corrugated cardboards. Many shape solutions used, for example, in paper lamps are based on these accordion-like foldings. Isamu Noguchi’s modern sculpture-like lamps that are based on Japanese tradition are one famous application of this.

Three basic origami- structures which I studied to form later on these sculpture works.

The paper sculptures in the image are formed of regular geometric folds. The hollow flower-like cylinders have straight basic foldings or folds, from which one can understand that “how” is a more essential question with them with regard to shape than “what”. The final shape for the work is often created as if a gift, because the creator does not know how to perceive in advance which shape is possible to realise with which structure. Here, I am not so much interested in the final result that can be seen in advance, but rather the delving into the possibilities of the structure as a process. The desire to know what all the structure can be applied to. With regard to these accordion-like works, it was interesting to notice that the works could be folded and thus transported in a fairly small space. They shrink and expand around their central axis. Such accordion foldings that collapse flat into a plane but maintain their surface area can also be formed from the same structure. (Images of fluted and folded paper flowers)

“Fractus” exhibition,  with folded art works, photo Jorma Kuula 1992


Sculptures composed of elements

The images presented here examine what takes place when a square-shaped paper is folded into rectangles from the centre of the paper towards the sides. First we fold as in the sketch drawing, diagonally from corner to corner, and then one more time the corners on top of each other. The triangle that was created in that way is folded three times into an accordion in the direction of the side. The pre-folded paper is opened and the foldings are forced to go back and forth inwards and outwards. The final result is carefully folded and opened into its final shape. We obtain a flexible three-dimensional paper element, which tightens itself into its shape and which can be used as a module for larger structures, as in here in the shape of a 6-pointed star.

This kind of a saddle-like square structure is also flexible and because of its structure tightens itself into its shape, which shows a triangle tetra’s proportions, in which the opposite sides are at a 90-degree angle to each other. Due to a flexible structure, folded star shapes can have fewer or more points and elements.

The final result is carefully folded and opened into its final shape. We obtain a flexible three-dimensional paper element, which tightens itself into its shape and which can be used as a module for larger structures, as in here in the shape of a 6-pointed star.

One experiential element in paper design geometry is studying and constructing various possible spread drawings of a paper cube. I remember that I was very surprised at how essential diagonal foldings were with regard to structure. The thought could be extended to how little diagonality is shown in modern European architecture, design or visual arts, which have been dominated by the somehow so stiff and unfounded horizontality and verticality. Attached are a few images of the possibilities of tracing the shape and structure of a cube with paper.

On working methods

The metamorphic tetrahedron, a set of elements. In a middle: two different drawings of possible unfold. Down under the second one as a folded box form.

Finally, we can return to the geometric structure by observing two working methods differing from each other, which have been used in courses discussing the structure and geometry of paper shapes (fibre packages) and when the dimensions of shape have been wanted to be traced onto paper. The premise of both methods is that a concrete object, whose external dimensions conform to the interior dimensions of the paper package, is packaged inside the paper, or a slab is built from a three-dimensional shape, a concrete application could be a cobbler’s dimensionally accurate model of a foot (shoe tree), with which the shoe can be drawn and produced.

It is good to try different working methods to see which one is the best for the current work and one’s own work. Paul Jackson, who has taught packaging design extensively, presents in detail in his book Structural Packaging (isbn 978-1856697538) a method, which is based on examining the proportions, shape and external dimensions of a carefully packaged object. The sides of a shape and their quantity is drawn onto a plane and numbered. These planes are combined in a logical manner in a carefully measured one-spoke spread drawing, i.e. blank. It is a good idea to learn the method phase by phase, because the final result is extremely certain and does not require any previous familiarisation with paper design, or a rather special talent.

On origami technique: Another working method that I have used and taught myself is based on the concrete wrapping of an objective and object in paper in many different ways and the utilisation of the information obtained from them later in the blank or spread drawing done based on it. The working method is freer, but at the same time more challenging. The user must already know the possibilities of paper better. With the method, more durable and/or open shapes with regard to their folding methods can be produced, because wrapping an object means that the material folds more back and forth and one on top of the other when following the object’s shape. In this way, the geometry of very organic or irregular shapes can be studied with origami, or such packaging methods, in which the content, the wrapped object itself, receives a more active role and keeps the package together with its volume.

Folding paper angularly was for me the inspiration point, from which a great view into concrete structuralism opened up.  Zeier, Franz ”Papier. Versuche zwischen Geometrie und Spiel” | 978-3-258-60095-6 |, I also saw how we can arrive at solutions that are similar at first glance by using many different paths. Every one can ponder whether the working method i.e. route matters, at least one has to change it if it leads to a dead end.

A continueing sketch or unrealized serial idea for the tetrahedron set of three-dimensional shapes.

Kai Rentola