Dodecahedron is a very unusual big figure, consisting of 12 similar faces, any of which is a faithful pentagon. To collect a dodecahedron with your own hands, it is not at all necessary to own special abilities of 3D modeling, even a child will handle this task. Slightly sniffs, and you will certainly succeed!

Needed materials and tools

• Sheet of snow-white and colored paper. The best density is 220 g / m 2. Very narrow paper very very much when assembling, and a very thick cardboard is torn off on bends.
• Dodecahedron scan (template).
• Narrow stationery knife or very sharp scissors.
• Conventional pencil or marker.
• Protractor.
• Long line.
• Watery glue.
• Tassel.

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1. If you have a printer, you can print the template from a sheet on a sheet, but it can be fully drawn without the help of others. Pentagons are built using the transport and ruler, the angle between the adjacent lines should be exactly 108 o, selecting the face of the face you can make a large or a small dodecahedron. The scan is 2 connected "flower" consisting of 6 figures. Be sure to leave small points, they are necessary for gluing.
2. Calretically cut out the workpiece with scissors or a knife on a special rubber rug, so as not to destroy the surface of the table. Further stroll through the folds of the folds to the sharp corner of the line, it will noticeably facilitate the assembly of the figure and make the faces more careful.
3. With the help of a tassel, apply slightly glue to the allowances and assemble the shape of flexing the edges inward. If you are going to make a dodecahedron with your own hands, and even the tape did not turn to my hand, cut the allowances of one half of the template in the form of elongated triangles, and on the twisters of the 2nd part, make small cuts. Then just stick the edges in the grooves, and the design will be tight enough.

The finished figure can be painted or decorate with stickers. The model of a huge size can be reincarnated into a unique calendar, because the number of sides corresponds to the number of months a year. If you are interested in Japanese applied art, you can make a dodecahedron with your own hands in the technique of modular origami.

1. Prepare 30 sheets of ordinary office paper. Excellent if they are colored and trilateral, you can choose several colors.
2. Manufacture of modules. At the level of thoughts, stretch the sheet into four monotonous stripes and fold the harmonica. Bend the angles in one direction in the back directions, the resulting figure should recall the parallelograms. It remains to proceed the workpiece by a short-lived diagonal. Make 30 modules and proceed to the assembly.
3. Dodecahedron has 10 nodes, each is collected from 3-parts. Prepare all parts and invest them in each other. So that the modules are not detour, fix the connections with clips, when you completely collect the figure, they can be removed.

When only you master the technique you like, you can teach to collect a dodecahedron with your own hands of your baby either comrade. After all, the manufacture of big figures is not only perfectly developing the motility of the fingers, and there is a spatial imagination.

Dodecahedron is a polyhedron consisting of 12 identical pentagons. This is a basic figure for a variety of crafts: from desktop calendars to openwork suspended lanterns.

There are other methods. For example, a pentagon can be built with the help of transport, but it does not guarantee accuracy. Most of the leggie way is to take a ready-made scheme, print it and on this "pattern" already make a shaker from suitable paper. But this method, despite the simplicity, is not always suitable - because sometimes it is necessary to make a dodecahedron of some particular size. You can enlarge one pentagon to the desired scale and print only it, then build a figure according to the diagram below.

But the "pattern" is not a readytery yet. How to make a dodecahedron of paper? To do this, you will need:

1. Paper suitable by density. It should not be too thin or too thick - it is desirable to 220 g / m², which is such a density of cardboard, which is sold in children's sets. Although it is quite possible to create volumetric figures from thick cardboard, you only need to pre-process all the bends - slightly cut or sell well so that they are good and smoothly bent.

2. Scissors, knitting needles or stationery knife

Tips for the manufacture of dodecahedron

Paper in places of folds is desirable to slowly sell the needle, a stupid side or something sharp, but not cutting. Neat smooth bends - half of success.

If there is no glue at hand, the dodecahedron can be assembled, as a constructor, making cuts to bend, and then simply inserting the sides alone to another.

If you collect a dodecahedron in modular technique (Instruction below), then the places of compounds are desirable to sample or fix with clips, since the design will become stable only after fixing the last module.

Dodecahedron in Origami

Origami module is an excellent base for a dodecahedron. How to make a dodecahedron of paper in modular technique? You will need 30 rectangular or square sheets of paper. Each of the leaves is folded in half, then each half must be bent in the opposite direction - it turns out the "harmonica" in four additions. Sometimes, if the sheet is not square, make the "harmonica" in three additions. As a result, you have a narrow promotional strip in your hands. Then, on each side of the rectangle on the narrow side you need to bend the corner. Corners fold in one direction - these are future fasteners that will be refunded in the "harmonic". Then bend the module into the diagonal diagonal from small lateral corners. Thus, one module for the origami of the dodecahedron is three-dimensional, it includes two ribs of the future figure and corners. When all modules are ready, you can start the assembly.

The assembly begins with one node for which you need to take three modules. Figure below is blue, pink and yellow origami modules. The assembly schemes are quite simple, and even beginners are easily coping with such figures.

What crafts can be made on the basis of a dodecahedron?

Each side of the dodecahedron of paper is a flat pentagon, which in itself can be the basis for a variety of and bizarre forms. For example, in the photo below the pentagon is replaced by a five-pointed star. There are no edges in such a figure, although it is assumed. How to make a dodecahedron of paper in the form of a star? Replace in the scan presented above, each pentagon of the required five-pointed figure and connect them not to the ribs, but along the vertices.

This photo shows star dodecahedron. At the heart of each "beam" lies all the same pentagon.

Instead of pentagonal pyramids, any bulk figure can be performed.

The photo below as pentagons are more complex origami modules, the schemes of which are interested in this technique will be able to be found in special literature.

In any case, mastering even the simplest scheme The assembly of the Dodecahedron will already give huge opportunities for creativity and finding their own options.

Dodecahedrome is called a bulk figure consisting of twelve pentagons. In order to get this figure, you must first draw it to the scan on tight paper, and then collect it from this scanner in space.

You will need

• - dense paper;
• - pencil;
• - Circle;
• - line;
• - Galnik;
• - a piece of thin wire;
• - scissors;
• - glue.

Instruction

1. Start work from the drawing of the central positive pentagon. To do this, draw a circle circle. Spend a diameter through its center. Now it needs to be divided into three parts. There is a theorem proving that trisction (that is, the distribution of the segment or an angle into three identical parts) with the help of a line without divisions and the circulation is unthinkable. Incidentally, measure the diameter of the lineup and divide it to three, and then notice the corresponding points on the dividing ruler on it, or measure it with a piece of thin wire, fold it threefold, after that straighten, impose on the diameter and notify points in the folding points.

2. As a result, the division of the diameter into three parts on it will turn out two points. Through one of them, swipe with the diameter with the help of the coal rebuilding. It will cross the circle in 2 places. From all of them, spend on the beam passing through the second point in diameter. They cross the circle back in 2 places, well, and the fifth place of intersection forms the diameter itself. It will remain only to combine them between themselves, and it will be a positive pentagon, inscribed in a circle.

3. In the same method, still eleven pentagons, placing them in this way, in order to turn out the figure similar to that shown in the figure. Turn the small petals to its faces to its faces facilitating gluing. After that cut it out and glue. What should happen in the end is shown in the articles header.

4. From the fact that dodecahedra is exactly twelve faces, in the form of this figure is allowed to produce volumetric, stable desktop calendars. To do this, first make up on all the edges of the calendar for one month, and only after that cut out and glue the figure. Also, such a calendar is allowed to generate mechanically by going to the reference below. The year will determine mechanically on the built-in server clock, and the names of the months and days of the week - on the settings of your browser.

Dodecahedrome A positive polyhedron is referred to, the faces of which are twelve positive pentagons. The simplest for the construction of a positive polyhedron is hexahedron or a cube, all other polyhedra are allowed to raise, writing or describing them near it. Dodecahedron is pervolored, describing it near Cuba.

Instruction

1. Build a cube with a rib length a. Calculate the length of the dodecahedron under the formula: M \u003d -A / 2 + AV5 / 2, where A is the length of the cube edge.

2. On the edge of SPRQ, swipe the K1L1 line connecting the middle of the ribs. At this line, postpone the length of the length M equal to the ribs of the cube. Through the sections of the segment, run perpendicular to the SPRQ faces.

3. Build a Pentagon ABCDE with AC and BE diagonals. AB \u003d BC \u003d a. Calculate the height of the ABC triangle and designate it S \u003d BN.

4. On the perpendiculars, detect the points, the distance from which to the middle of the edges is S, i.e. ll1 \u003d kk1 \u003d s. Combine now detected points with cube tops.

5. Repeat the construction of 2 and 4 for any face, as a result you will have a positive polyhedron described near Cuba - Dodecahedron.

Video on the topic

Dodecahedron is a very unusual volumetric figure, consisting of 12 identical faces, each of which is to collect a dodecahedron with their own hands, not even necessarily possess special skills with this task even a child can cope. A little snarling, and you will definitely work out!

Necessary materials and tools

• Sheet of white and colored paper. The optimal density is 220 g / m 2. Very thin paper is too much when the assembly is assembling, and a very thick cardboard is excreted on bends.
• Dodecahedron scan (template).
• Thin or very sharp scissors.
• Simple pencil or marker.
• Protractor.
• Long line.
• Liquid glue.
• Tassel.

Instruction

1. If you have a printer, you can print the template immediately on the sheet, but it can be performed independently. Pentagons are built using the transport and line, the angle between adjacent lines should be exactly 108 o, selecting the face of the face you can make a large or small dodecahedron. The scan is 2 connected "flower" consisting of 6 figures. Be sure to leave small allowances, they are needed for gluing.
2. Carefully cut the workpiece with scissors or a knife on a special way to not damage the surface of the table. Next, go through the folds of the folds with a sharp corner of the line, this will noticeably facilitate the assembly of the figure and make the edges more neat.
3. With the help of a brush, apply a little glue to the allowances and assemble the shape flexing the edges inside. If you decide to make a dodecahedron with your own hands, and at hand I didn't even have a scotch, cut the allowances of one half of the template in the form of elongated triangles, and on the sequins of the second part, make small cuts. Then simply insert the edges in the grooves, and the design will be quite firmly held.

The finished figure can be painted or decorated with stickers. The large-size model can be turned into an original calendar, because the number of parties corresponds to the number of months a year. If you are interested in Japanese, you can make a dodecahedron with your own hands in the technique of modular origami.

1. Prepare 30 sheets of ordinary office paper. Well, if they are colored and double sided, you can choose a few shades.
2. Making modules. Mentally draw a sheet into four identical stripes and fold the harmonica. Bend the angles in one direction in opposite directions, the resulting figure should resemble parallelograms. It remains to proceed the workpiece on a short diagonal. Make 30 modules and proceed to the assembly.
3. Dodecahedron has 10 nodes, each is collected from three elements. Prepare all parts and invest them in each other. So that the modules are not trapped, fix the joints with paper with paper, when you completely collect the figure, they can be removed.

When only you master the technique you like, you can teach to collect a dodecahedron with your own hands of your child or comrade. After all, the manufacture of bulk figures is not only well developing the motility of the fingers, but also forms spatial imagination.

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From the history of dodecahedron

Everyone who studied at school studied geometry, someone loved her, and someone was not very, and someone would only have to get to know this science. And, of course, everyone asked to draw or collect various geometric shapes, and then evaluated best job. But, unfortunately, not all teachers tell about the origin of the geometric figures, for which they need, what value are and where they are applied. And the figures have a very rich history, they are important as well as any discoveries in our world. And they meet everywhere, we just not always notice them. Today we will tell you about Dodecahedra.

The word Dodecahedron has a Greek origin and consists of 2 words: DODEKA (twelve) and Hedra (edge). Dodecahedron has 12 faces, 20 vertices, each of which converges 3 ribs and 30 Ryubers. The sum of flat corners is 324 °. This is a twelve brand, which is composed of twelve regular pentagons. Dodecahedron Right polyhedron, it has three star forms.

About Dodecahedra was known already in ancient times. For example, pupils of the Pythagorean school were forbidden to pronounce this word outside the school, as they could lose their lives for it. These figures were treated as a holy figure, they were even afraid of something to say. Only two hundred years later, at the time of Plato, they began to speak very carefully about this figure. It was forbidden to say something superfluous, the more offensive or dismissive. They believed that the Dodecahedron is in the energy field of people and is the highest form of human consciousness. In addition, it was believed that people live inside a huge dodecahedron, in which our universe is located and when a person's mind reaches the very limit of space of space, it stones on a dodecahedron, closed in the sphere.

Dodecahedron in our lives

Where can I meet a dodecahedron? Think carefully! Probably almost everyone saw him as a random number generator, for example, on TV in the game Lotto or desktop role-playing games. Dodecahedron can be found in the game "Pentor", the world of which is presented in the form of this figure. And, of course, everyone heard about the Pentagon, this building of the US Department of Defense has the form of the right pentagon.

In August 2006, when applied to the distribution cards of dark matter in the accumulation of galaxies, conclusions were made that our universe looks like a set of infinitely repeated dodecahedra.

The correct polyhedra has always been attracted by the perfection of their forms, it would seem impossible to symmetry. Some of these bodies are found in nature, for example, in the form of crystals, others can be in the form of viruses or the simplest microorganisms.

You can collect this amazing figure using our dodecahedron sweeps.

Dodecahedron scan of paper or cardboard

Scheme of the correct dodecahedron	Dodecahedron scheme with formulas	Dodecahedra scheme with great discoveries of humanity