Handicap fLEXAGON. How to make a volume craft?

Paper crafts are a whole world of creative diversity. Many pieces of paper are invented by mathematicians. For example, the world-famous flash-box was also invented by Princeton University student Arthur Stone in 1939. What is interesting about flexagon? How to make a variety of flex-boxes and please the children?

Funny hand-made paper

The very Latin word ( flectere ), which is the basis of the name, means to bend or fold. Therefore, a flexagon is a polygon that can be created from a regular strip of white paper. Each time we bend the polygon, we find a new plane.

What does flexingon look like? How to make this figure correctly? Usually make a hexagonal flat flexagon, since it is the simplest. Using a variety of drawings on these planes, we can please the children with an unusual craftsmanship, and to attract them to create both a flat and a three-dimensional shape is also useful.

Flexagons: how to make of paper?

Where to begin? So, we decided to create a flex-box. How to make a craft quickly? The polygon is easily and quickly assembled from one sheet of any paper, but it is advisable to choose not too soft. Flexaxons of a quadrangular form are called tetraflexons. A figure that has the shape of a hexagon is called a hexaflexagon. Each of its surfaces has 6 sectors-triangles. There are also octaflexars (8 sides) and dodecaflex (10 sides). How to make a flex paper from paper? Schemes are very diverse. Let's consider the simplest, which makes a conventional hexaflexagon. This scheme is used most often.

It is easy to draw it yourself, because it consists only of a group of regular triangles. But you can use the already painted scheme, which is the first time easier to collect hand-made articles. After the circuit is cut out, fold the sheet in half and add it in stages, bending down each triangle that forms part of a single plane. When the flexagon is fully assembled, glue the last part.

Each of the 4 surfaces will have its own drawing. Having studied this scheme, you can go on to work creatively. On the usual sheet of paper we draw the same triangles. Then number the sectors that form the plane. Triangles, according to the instruction, must be bent downward, forming the necessary polygon. But everyone chooses his own way, how to fold more conveniently. Similar to this scheme, any polygon-flexagon is assembled. More complex schemes of figures are better to master gradually.

Postcard-flexagon

The mathematical model-flexagon will certainly interest the child. This surprising property of paper can be applied in a variety of ways. On the surface of the finished figure we depict the heroes of children's cartoons and present the child with a brilliant proof that mathematical models can be interesting.

And also you can come up with an excellent and unusual postcard, and this is not a joke. How to make a postcard-flex-box? If you draw on the surfaces of congratulatory words for the child and Christmas toys, it will be an excellent gift for the New Year. But if the drawings do not work well for you, find another way out. You can simply cut out the picture you liked and divide it into equal triangles, which then have to be gently glued on each sector of the craft

Bulky products - a variety of harmony

There are still three-dimensional figures. How to make a volumetric flexbon from a paper? To do this, you need to take an example of a ready-made schema that consists of 10 equilateral triangles serving as sectors. This figure is called a trihexaflexagon - that is, the given three-dimensional hexagon has three surfaces. Of course, this is not the limit. The model can contain both 4 and 5 surfaces, and even 10. These flexags are more interesting, although based on the same idea. But to collect such a miracle is not so simple. The main rule for building a model is to follow the instructions. A hexaflexagon scheme with 4 surfaces will look like this:

And here is an example, according to which an even more grandiose figure is going to gather - nonagexaflexagon. That is a voluminous flex-box with six corners, and the surfaces are already 9. This toy is already for adults, the child can not master such a model, at least without the help of the parents.

To understand the intricacies of the scheme of this voluminous figure, it takes time. The workpiece is better to decorate with different colors at once, so as not to get confused when assembling. Try it!