A dodecahedron is a regular polyhedron made up of twelve regular pentagons. This spectacular three-dimensional figure has a center of symmetry called the center of the dodecahedron. In addition, it contains fifteen planes of symmetry (in each face, any of them passes through the middle of the opposite edge and the vertex) and fifteen axes of symmetry (intersecting the midpoints of parallel opposite edges). Each of the vertices of the dodecahedron is the vertex of three pentagons of regular shape.

The design received its name from the number of faces included in it (traditionally, the ancient Greeks gave polyhedrons names reflecting the number of faces that make up the structure of the figure). Thus, the concept of “dodecahedron” is formed from the meanings of two words: “dodeca” (twelve) and “hedra” (face). The figure belongs to one of the five Platonic solids (along with tetrahedron, octahedron, hexahedron (cube) and). Interestingly, according to numerous historical documents, all of them were actively used by the inhabitants of Ancient Greece in the form of table dice and were made from a wide variety of materials.

Regular polyhedra have always attracted people with their beauty, organic nature and extraordinary perfection of forms, but the dodecahedron has a special history, which from year to year acquires new, sometimes completely mystical, facts. Representatives of many civilizations saw in it a supernatural and mysterious essence, claiming that: “Many things grow from the number twelve.” In the territories of ancient destroyed states, small figurines in the form of dodecahedrons made of bronze, stone or bone are still found. In addition, during excavations in the lands of modern England, France, Germany, Hungary, and Italy, archaeologists discovered several hundred so-called “Roman dodecahedrons” dating back to the 2nd-3rd centuries AD. The main dimensions of the figures range from four to eleven centimeters, and they are distinguished by the most incredible patterns, textures and execution techniques. The version put forward back in the time of Plato that the Universe is a huge dodecahedron was confirmed at the beginning of the 21st century. After a thorough analysis of the data obtained using WMAP (NASA's multifunctional spacecraft), scientists agreed with the assumption of ancient Greek astronomers, mathematicians and physicists, who at one time dealt with the study of the celestial sphere and its structure. Moreover, modern researchers believe that our Universe is an infinitely repeating set of dodecahedrons.

How to make a regular dodecahedron with your own hands

Today, the design of this figure is reflected in many forms of artistic creativity, architecture and construction. Folk craftsmen make unusually beautiful origami in the form of openwork dodecahedrons from colored or white paper, and they make original ones from cardboard, etc.). On sale you can purchase ready-made kits containing everything you need to make souvenirs, but the most interesting thing is to do the entire process of work with your own hands, from building individual parts to assembling the finished structure.

Materials:

In order to make a regular dodecahedron from cardboard, you need the material itself and available tools:

• scissors,
• pencil,
• eraser,
• ruler,
• glue.

It’s good to have a dull knife or some kind of device for bending seam allowances, but if you don’t have them, then a metal ruler or the same scissors will do just fine.

How to make a stellated dodecahedron

Stellated dodecahedrons have a more complex structure compared to ordinary ones. These polyhedra are divided into small (of the first extension), medium (of the second extension) and large (the last stellate shape of the regular dodecahedron). Each of them has its own design features and assembly. To work, you will need the same materials and tools as for making a standard dodecahedron. If you decide to make the first option (small dodecahedron), then you need to build a drawing of the first element, which will become the basis for the entire structure (later it will be glued or parts assembled using paper clips).

Creating crafts with your own hands is interesting not only for children, but also for adults. However, a sufficient number of models have been invented for adults, which differ in the complexity of implementation and the time spent on their creation. Recently, adults and children have become interested in creating complex geometric shapes. This type of figure includes the icosahedron, which is a regular polygon and is one of the Platonic solids - regular polyhedra. This figure has 20 triangular faces (equilateral triangles), 30 edges and 12 vertices, which are the junction of 5 edges. Assembling a correct icosahedron from paper is quite difficult, but interesting. If you are passionate about origami, then making a paper icosahedron with your own hands will not be difficult for you. It is made from colored, corrugated paper, foil, and wrapping paper for flowers. Using a variety of materials, you can add even greater beauty and effectiveness to your icosahedron. Everything depends only on the imagination of its creator and the available material on the table.

We offer you several options for icosahedron developments, which can be printed, transferred to thick paper and cardboard, folded along the lines and glued.

How to make an icosahedron from paper: diagram

In order to assemble an icosahedron from a sheet of paper or cardboard, you must first prepare the following materials:

• icosahedron layout;
• PVA glue;
• scissors;
• ruler.

When creating an icosahedron, it is important to pay special attention to the process of bending all the parts: in order to bend the paper evenly, you can use a regular ruler.

It is noteworthy that the icosahedron can also be found in everyday life. For example, a soccer ball is made in the shape of a truncated icosahedron (a polyhedron consisting of 12 pentagons and 20 hexagons of regular shape). This is especially visible if you color the resulting icosahedron in black and white, like the ball itself.

You can make such a soccer ball yourself by first printing out a scan of a truncated icosahedron in 2 copies:

Creating an icosahedron with your own hands is an interesting process that requires thoughtfulness, patience and a lot of paper. However, the final result will please the eye for a long time. The icosahedron can be given to a child to play with if he has already reached the age of three. By playing with such a complex geometric figure, he will develop not only imaginative thinking and spatial skills, but also become acquainted with the world of geometry. If an adult decides to create an icosahedron on his own, then such a creative process of constructing an icosahedron will allow him to pass the time and also show off to his loved ones his ability to create complex shapes.

The dodecahedron is a very unusual large figure, consisting of 12 similar faces, each of which is a regular pentagon. To assemble a dodecahedron with your own hands, you don’t necessarily need to have special 3D modeling skills; even a child can handle this task. A little skill, and you will certainly succeed!

Necessary materials and tools

• A sheet of white and colored paper. The best density is 220 g/m2. Very narrow paper gets very wrinkled when assembled, and very thick cardboard breaks at the folds.
• Development of a dodecahedron (template).
• A narrow stationery knife or very sharp scissors.
• A regular pencil or marker.
• Protractor.
• A long ruler.
• Watery glue.
• Brush.

annotation

1. If you have a printer, you can print the template directly on a sheet of paper, but you can completely draw it without the help of others. Pentagons are constructed using a protractor and a ruler; the angle between adjacent lines should be exactly 108°; by selecting the length of the edge, you can make a large or small dodecahedron. The development consists of 2 connected “flowers”, consisting of 6 figures. Be sure to leave small allowances, they are necessary for gluing.
2. Carefully cut the workpiece with scissors or a knife on a special rubber mat so as not to destroy the surface of the table. Next, walk along the bends with a sharp angle of a ruler, this will significantly facilitate the assembly of the figure and make the edges more careful.
3. Using a brush, apply a little glue to the seam allowances and assemble the shape by folding the edges inward. If you are planning to make a dodecahedron with your own hands, but don’t even have tape on hand, cut out the allowances of one half of the template in the form of elongated triangles, and make small cuts on the folds of the second part. Then just stick the edges into the grooves, and the structure will hold quite tightly.

The finished figure can be painted or decorated with stickers. The huge model can be turned into a unique calendar, because the number of sides corresponds to the number of months in the year. If you are interested in Japanese arts and crafts, you can make a dodecahedron with your own hands using the modular origami technique.

1. Prepare 30 sheets of ordinary office paper. It’s great if they are colored and double-sided, you can choose several colors.
2. Manufacturing of modules. At the level of thoughts, draw the sheet into four uniform stripes and fold it like an accordion. Bend the corners to one side in the opposite direction, the resulting figure should resemble a parallelogram. All that remains is to bend the workpiece along a short diagonal. Make 30 modules and start assembling.
3. The dodecahedron has 10 nodes, each assembled from 3 parts. Prepare all the parts and nest them inside each other. To prevent the modules from moving apart, secure the connections with paper clips; when you have completely assembled the figure, they can be removed.

Once you have mastered the technique you like, you can teach your child or friend how to assemble a dodecahedron with your own hands. After all, making large figures not only perfectly develops finger motor skills, but also forms spatial imagination.

The dodecahedron is a very unusual three-dimensional figure, consisting of 12 identical faces, each of which represents. To assemble a dodecahedron with your own hands, it is not at all necessary to have special skills; even a child can cope with this task. A little skill, and you will definitely succeed!

Required materials and tools

• A sheet of white and colored paper. The optimal density is 220 g/m2. Very thin paper wrinkles too much when folded, and very thick cardboard breaks at the folds.
• Development of a dodecahedron (template).
• Thin or very sharp scissors.
• A simple pencil or marker.
• Protractor.
• Long ruler.
• Liquid glue.
• Brush.

Instructions

1. If you have a printer, you can print the template directly on a sheet of paper, but you can easily draw it yourself. Pentagons are constructed using a protractor and a ruler; the angle between adjacent lines should be exactly 108°; by selecting the length of the edge, you can make a large or small dodecahedron. The development consists of 2 connected “flowers”, consisting of 6 figures. Be sure to leave small allowances, they are needed for gluing.
2. Carefully cut the workpiece with scissors or a special knife so as not to damage the surface of the table. Next, go over the folds with a sharp angle of a ruler, this will make it much easier to assemble the figure and make the edges more neat.
3. Using a brush, apply a little glue to the seam allowances and assemble the shape by folding the edges inward. If you decide to make a dodecahedron with your own hands, but don’t even have tape on hand, cut out the allowances of one half of the template in the form of elongated triangles, and make small cuts on the folds of the second part. Then simply insert the edges into the grooves, and the structure will hold quite firmly.

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

1. Prepare 30 sheets of regular office paper. It’s good if they are colored and double-sided, you can choose several shades.
2. Manufacturing of modules. Mentally draw the sheet into four identical strips and fold it like an accordion. Bend the corners to one side in opposite directions, the resulting figure should resemble a parallelogram. All that remains is to bend the workpiece along a short diagonal. Make 30 modules and start assembling.
3. The dodecahedron has 10 nodes, each assembled from three elements. Prepare all the parts and nest them inside each other. To prevent the modules from moving apart, secure the joints with paper clips; when you have completely assembled the figure, they can be removed.

Once you have mastered the technique you like, you can teach your child or friend how to assemble a dodecahedron with your own hands. After all, making three-dimensional figures not only develops fine motor skills of the fingers, but also develops spatial imagination.

A dodecahedron is a three-dimensional figure consisting of twelve pentagons. In order to obtain this figure, you must first draw its development on thick paper, and then assemble it from this development in space.

You will need

• – thick paper;
• - pencil;
• – compass;
• - ruler;
• – square;
• – a piece of thin wire;
• - scissors;
• - glue.

Instructions

1. Start by drawing a central positive pentagon. To do this, draw a circle with a compass. Draw a diameter through its center. Now it needs to be divided into three parts. There is a theorem that proves that trisection (that is, the distribution of a segment or angle into three identical parts) using a ruler without divisions and a compass is unthinkable. Therefore, either measure the diameter with a ruler and divide it into three, and then mark the corresponding points on it according to the divisions of the ruler, or measure it with a piece of thin wire, fold it in three, then straighten it, put it on the diameter and mark the points at the bends.

2. As a result of dividing the diameter into three parts, you will get two points on it. Through one of them, draw a perpendicular to the diameter using a square. It will intersect the circle in 2 places. From each of them, draw a ray passing through the second point on the diameter. They will intersect the circle in 2 more places, and the fifth place of intersection forms the diameter itself. All that remains is to combine them with each other, and you will get a positive pentagon inscribed in a circle.

3. Using the same method, draw eleven more pentagons, arranging them in such a way as to form a figure similar to that shown in the figure. Draw small petals on the sides to make gluing easier. After that, cut it out and glue it together. What should happen in the end is shown in the illustration in the title of the article.

4. Since the dodecahedron has exactly twelve faces, it is possible to produce voluminous, stable table calendars in the form of this figure. To do this, first make a calendar for one month on all of the faces, and only after that cut out and glue the figure. You can also generate such a calendar mechanically by clicking on the link below. The year will be determined mechanically by the server’s built-in clock, and the language for the names of months and days of the week will be determined by the settings of your browser.

Dodecahedron is called a positive polyhedron, the faces of which are twelve positive pentagons. The simplest positive polyhedron to construct is a hexahedron or cube; all other polyhedra can be constructed by inscribing or describing them around it. A dodecahedron can be constructed by describing it around a cube.

Instructions

1. Construct a cube with edge length a. Calculate the length of the dodecahedron under construction using the formula: m = -a/2 +av5/2, where a is the length of the edge of the cube.

2. At the edge of SPRQ, draw a line K1L1 connecting the midpoints of the edges. On this line, lay a segment of length m, equidistant from the edges of the cube. Draw perpendiculars through the ends of the segment to the face SPRQ.

3. Construct a pentagon ABCDE with diagonals AC and BE. AB = BC = a. Calculate the height of triangle ABC and denote it s = BN.

4. Find points on the perpendiculars, the distance from which to the midpoints of the edges is equal to s, i.e. LL1 = KK1 = s. Combine the now discovered points with the vertices of the cube.

5. Repeat constructions 2 and 4 for each face, as a result you will get a positive polyhedron described around the cube - a dodecahedron.

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