How to make a regular icosahedron from paper diagram. How to make three-dimensional geometric shapes from paper (diagrams, templates)? How to make a Sonobe module

One of the most popular areas in origami is 3D modeling. Creating three-dimensional figures captures the attention of not only children, but also adults. If you have already mastered the simplest patterns and techniques and learned how to make at least a cube out of paper, you can move on to more complex models. It is best to practice creating the so-called "Platonic solids". There are only five of them: tetrahedron, icosahedron, hexahedron, dodecahedron and octahedron. All figures are based on the simplest. Today you will learn how to make an icosahedron from paper.

List of materials and tools

One sheet of thin colored cardboard (preferred density is 220 g/m2).
Sharp scissors or a utility knife.
Simple NV.
Long wooden ruler (at least 20 cm).
Eraser.
Liquid PVA glue or pencil.
Brush.

Instructions

If you fully understand how to make an icosahedron from paper, you can practice assembling a more complex model - a truncated icosahedron. This figure consists of 32 faces: 12 equilateral pentagons and 20 B finished form and when painted correctly, it is very reminiscent of paper. The assembly principle is similar, the only differences are in the template. The development of a truncated icosahedron is very difficult to construct, so it is better to print it on a printer. You should choose very thick paper, otherwise the figure will not hold its shape, and sagging may form in places where pressure is applied.

Origami and 3D modeling are a great way to while away a friendly or family evening. Such activities create a good intellectual background and help develop spatial imagination.

Many people like to create fakes from paper, and this does not depend at all on their age; both children and adults are susceptible to this activity. The only difference is that adults like to create more complex shapes. For some reason, they are especially often created geometric figures. In our article we will tell you how to make an icosahedron out of paper. This is the name given to a complex, regular polygon, which has as many as twenty triangular faces and thirty edges. As you may have noted, this figure is quite complex in appearance. Even if you are new to origami, our method will not seem complicated and you can easily glue it from paper.

Among the variety of materials that are used to make it, you can take the following: corrugated paper, foil, paper for gift wrapping or flowers. With the help of various other materials, you can improve your figure and decorate it. Do not limit your imagination in this matter, and it will help you.

Before you begin, you need to prepare. For this you may find the following materials useful:

A blank figure that needs to be transferred to the material for our figure.
Glue. It's best to use PVA - it dries long enough for you to correct mistakes when gluing.
Scissors.
Ruler.

Once you have obtained all the necessary components, you can begin work. Now we will present a diagram by which this figure can be made:

So, our figurine is ready and now you can start decorating it. It can be painted with paints or pencils, or hung on a string. Various sparkles and pieces of rain are also perfect. Very often, such decoration can be used as a toy on christmas tree. Besides this, you can do a very funny thing using icosahedrons, namely - soccer ball, which is a truncated figure. If you examine it carefully, you will notice that it consists of twelve pentagons and twenty hexagons, which are of the same size. The decorated figurine will look great, and different colors simple elements will show this difference even more strongly.

If this idea intrigues you, then below we present a development with which you can make a ball:

As you can see, creating paper figures is a very interesting process. Once you learn how to make an icosahedron, you can move on to other, more complex geometric shapes. This is especially useful for children who can early years develop spatial thinking, study geometry and improve fine motor skills. If the child is very small, then the help of parents may be required, however, he will happily play with the finished toy on his own. Nevertheless, this activity will also be useful for adults - this is a great hobby that can help you relax or just pass the time. If you like work that is not painstaking and requires attention, then this activity is just what you need.

We hope that our article on how to make an icosahedron from paper was of interest to you. Perhaps it is with this figure that you will start making paper crafts. Good luck and success in all your endeavors!

Video lessons

To make three-dimensional geometric shapes, the main thing is to have templates that can be cut out and then glued.

Can be made from white or colored paper. You can cut it out of paper with any designs or numbers.

I propose to make an unusual three-dimensional figure using the origami technique. Watch the video:

So that children can better remember what geometric shapes there are and know what they are called, you can make them out of thick paper or cardboard volumetric geometric shapes. By the way, you can use them to make beautiful gift wrapping.

You will need:

thick paper or cardboard (preferably colored);
ruler;
pencil;
scissors;
glue (preferably PVA).

The most difficult thing is to develop and draw layouts; you need at least basic knowledge of drawing. You can take ready-made designs and print them on a printer.

To keep the fold line straight and sharp, you can use a blunt needle and a metal ruler. When drawing a line, the needle must be bent strongly in the direction of movement, almost laying it on its side.

This is a development of a trihedral pyramid

This is a cube scan

This is the development of an octahedron (tetrahedral pyramid)

This is the development of a dodecahedron

This is the development of an icosahedron

Here you can find templates for more complex figures (Platonic Solids, Archimedean Solids, polyhedra, polyhedra, different types pyramids and prisms, simple and oblique paper models).

Volumetric geometric shapes are the best way baby's exploration of the world around him. Excellent teaching material/excellent tutorial for the study of geometric figures - this is just volumetric figures. This way, geometric shapes are better remembered.

The best material for making such three-dimensional figures is thick paper (can be colored) or cardboard.

For production, in addition to paper, you will also need a pencil with a ruler, as well as scissors and glue (cut and glue the developments).

You need to draw the scans in a similar way and cut them out:

After which they need to be glued edge to edge.

You should get the following type of volumetric geometric shapes:

Here are several schemes by which you can make three-dimensional geometric shapes.

The simplest one is tetrahedron.

It will be a little more difficult to make octahedron.

But this three-dimensional figure - dodecahedron.

Another one - icosahedron.

More details about making three-dimensional figures can be found here.

This is what three-dimensional figures look like not assembled:

And this is what the finished ones look like:

You can make a lot out of three-dimensional geometric shapes original crafts, including gift packaging.

Before you start making three-dimensional geometric shapes, you need to imagine (or know what it looks like) the figure in 3D dimension: how many faces does this or that figure have.

First you need to correctly draw a figure on paper along the edges that must be connected to each other. Each shape has edges that have a specific shape: square, triangle, rectangle, rhombus, hexagon, circle, etc.

It is very important that the length of the edges of the figure that will be connected to each other are the same length, so that no problems arise during the connection. If the figure consists of identical faces, I would suggest making a template while drawing and using this template. You can also download ready-made templates from the Internet, print them, bend them along the lines and connect (glue) them together.

Cone Pattern:

Pyramid template:

You will need to make three-dimensional geometric shapes both in school classes and for studying shapes with kids. This process can be turned into a game by making dense three-dimensional geometric shapes out of cardboard.

To make the figures we will need a pencil, ruler, colored cardboard, glue.

You can print out diagrams from the Internet, then apply them to thick paper, not forgetting about the fold lines that will be glued together.

You can use the following schemes:

But they are already in finished form.

This way you can spend time with your baby having fun and usefully studying geometric shapes.

By making three-dimensional figures from paper yourself, you can not only use them for entertainment, but also for learning.

For example, you can clearly show your child what a particular figure looks like and let him hold it in his hands.

Or you can print out diagrams with special symbols for training purposes.

So I suggest you familiarize yourself with this topic below dodecahedron, both simple and with small drawings, which will only attract the baby’s attention and make learning more fun and entertaining.

Also the diagram Cuba Can be used to teach numbers.

Scheme pyramids can help you understand the formulas that apply to a given figure.

In addition, I suggest that you familiarize yourself with the diagram octahedron.

Scheme tetrahedron Among other things, it will help you learn colors.

As you understand, the above templates must be printed, cut out, bent along the lines, and glued along special narrow strips adjacent to selected sides.

Three-dimensional geometric figures are simply necessary when teaching: they provide students with the opportunity to hold them in their hands and examine them, which is an important part of the educational process; they are simply necessary as a tool for studying the famous Euler theorem - clearly demonstrating that even with deformations and curvatures, the number of faces of a polyhedron , and therefore Euler’s relation, will remain unchanged:

In addition, solid figures can be an excellent tool to help explain to students how to find the surface area of a polyhedron.

So, using the templates below you can easily make the following shapes:

Triangular Prism

N-gonal prism

Tetrahedron

A relief polyhedron is called a positive polyhedron if all its faces are equal, positive polygons, and an identical number of edges converge at its entire vertex. There are five regular polyhedra - tetrahedron, octahedron, icosahedron, hexahedron (cube) and dodecahedron. An icosahedron is a polyhedron whose faces are twenty equal right triangles.

Instructions

1. For building icosahedron Let's use the construction of a cube. Let us denote one of its faces as SPRQ.

2. Draw two segments AA1 and BB1 so that they connect the midpoints of the edges of the cube, that is, as = AP = A1R = A1Q = BS = BQ.

3. On segments AA1 and BB1, lay equal segments CC1 and DD1 of length n so that their ends are at equal distances from the edges of the cube, i.e. BD = B1D1 = AC = A1C1.

4. Segments CC1 and DD1 are the edges of the construction icosahedron A. By constructing the segments CD and C1D, you will get one of the faces icosahedron a – CC1D.

5. Repeat constructions 2, 3 and 4 for all faces of the cube - as a result you will get a regular polyhedron inscribed in the cube - icosahedron. With the help of the hexahedron it is possible to construct any regular polyhedron.

An icosahedron is a regular polygon. Such a geometric figure has 30 edges, 20 triangular faces and 12 vertices, which are the junction of five edges. Assembling an icosahedron from paper is quite difficult, but very exciting. It can be made from corrugated, packaging or colored paper or foil. Applying different materials, you can add even greater impact and beauty to your icosahedron.

You will need

– layout of the icosahedron;
- paper;
- scissors;
- ruler;
- PVA glue.

Instructions

1. Print out the icosahedron layout on a piece of paper, then cut it out along the dotted lines. This is necessary in order to leave free space for gluing parts of the figure to each other. Try to cut out the icosahedron as leisurely as possible; on the contrary, at the slightest shift, your craft will end up looking ugly. The need for very neat cutting is due to the fact that all triangles in a regular icosahedron have identical sides. Consequently, if any side begins to differ in its length, as a result such a discrepancy in size will be invisible.

2. Fold the icosahedron along solid lines, then use glue to glue the places outlined by the dotted line and connect the adjacent sides of the triangles with each other. For a tighter fixation, each glued side must be kept in this state for 20 seconds. It is true that all other sides of the icosahedron should be glued in the same way. The last two ribs are the hardest to glue because they require patience and skill to join them together. Your paper icosahedron is ready.

3. Such a geometric figure can be seen in Everyday life. For example, a soccer ball is made in the shape of a truncated icosahedron (a polyhedron consisting of 20 hexagons and 12 pentagons). This becomes especially invisible if the resulting icosahedron is colored in black and white color. You can make a soccer ball out of paper yourself by printing out a scan of a truncated icosahedron in 2 copies in advance.

4. Making an icosahedron from paper is an interesting process that requires patience, thoughtfulness and a lot of paper. But the resulting result will please the eye for a long time. A paper icosahedron can be given as a developmental toy to a child who has reached the age of 3. By playing with this geometric figure, the baby will develop not only spatial skills and imaginative thinking, but also become more familiar with the world of geometry. For an adult creative process How to construct a paper icosahedron with your own hands will allow you to pass the time, and also amaze your loved ones with the knowledge of making difficult figures.

Helpful advice
When making a paper icosahedron, you need to pay special attention to the process of bending its sides. To bend the paper evenly, you can use an ordinary ruler.

The octahedron is one of the four true polyhedra that people have given magical meaning back in ancient times. This polyhedron symbolized air. A demonstration model of the octahedron can be made from thick paper or wire.

You will need

– thick paper or cardboard;
- ruler;
- pencil;
– protractor;
- scissors;
- PVA glue.

Instructions

1. The octahedron has eight faces, all of which are an equilateral triangle. In geometry, an octahedron is usually constructed, inscribed in a cube or described around it. To make a model of this geometric body, difficult calculations are not required. The octahedron will consist of 2 identical tetrahedral pyramids glued together.

2. Draw a square on a piece of paper. On one of its sides, construct a positive triangle in which all sides are equal and all of the angles are 60°. It is convenient to construct a triangle using a protractor, setting aside 60° corners of a square adjacent to the same side. Draw rays through the marks. The point from the intersection will be the third angle, and in the future - the top of the pyramid. Build the same triangles on the remaining sides of the square.

3. You will have to glue the pyramid together. This will require allowances. Four allowances are enough, one for each triangle. Cut out what you have. Make a second similar piece. Fold the fold lines to the wrong side.

4. Fold each of the triangles to the wrong side. Apply PVA glue to the allowances. Glue two identical pyramids together and let them dry.

5. Now we need to glue the pyramids together. Spread the square bottom of one of them with glue, press the bottom of the 2nd one, aligning the sides and corners. Let the octahedron dry.

6. To make a wire octahedron model, you will need a cardboard or wooden square. However, you can get by with an ordinary triangle - in order to bend the workpiece at a right angle, it is absolutely sufficient. Bend the wire into a square.

7. Cut 4 identical pieces of wire the size of 2 sides of the square, plus an allowance for attaching them at 2 points to each other, and, if necessary, attaching them to the corners of the square. It depends on the wire. If the material can be soldered, the length of the edges is equal to twice the side of the square without any allowances.

8. Find the middle of the piece, wind or solder it to the corner of the square. Attach the remaining pieces in the same way. Connect the ends of the ribs on one side of the square base to each other. Positive triangles will appear by themselves. Perform the same operation with the ends of the ribs located on the other side of the base. The octahedron is ready.

Helpful advice
For similar models, you must choose the wire that holds its shape well.

The art of origami came to us from Ancient China. At the dawn of their formation, figures of animals and birds were made from paper. But today it is possible to create not only them, but also complex geometric figures.

You will need

– a sheet of A4 paper
- scissors

Instructions

1. To produce a three-dimensional geometric figure, an octahedron, you need a square sheet of paper. You can make it from an ordinary A4 sheet. To do this, bend the upper right or left corner of the sheet to the opposite side. Make a note on a piece of paper. Draw a line parallel to the tight side of the sheet along the mark you made. Cut off the unwanted piece of paper. Fold the square in half.

2. Place the top right corner on the center fold. Align the top left corner so that the fold line goes through the attached top right corner.

3. Fold the bottom left corner of the square toward the center line. Aligning the bottom right corner similar to the top corners, make a fold. After which the workpiece must be overturned.

4. Fold the bottom right corner of the piece and the top left corner to the center fold. Iron the workpiece with your hand and turn it over to the other side.

5. Align the top and bottom sides with the resulting fold line. Smooth the workpiece with your hand.

6. Bend the sides of the figure towards the middle line of the square. Flip the piece over to the opposite side.

7. Fold the piece from bottom to top along a horizontal line. The result should be a figure resembling the Latin letter “V”.

8. Fold the left side down along the left side of the center triangle. Fold the right side down along the right side of the central triangle.

9. Make stripes on the top sides of the figure. The fold point of the strips will begin at the bottom point of the inside cutout of the "V".

10. Fold the upper left corner to the fold line of the strip. Then fold the strip down. Fold the right corner and strip in the same way.

11. Fold the left side down.

12. The illustration shows the pockets and inserts for assembling the octahedron.

13. To construct an octahedron, you need to make 4 such modules. Align the two modules at an angle, tucking the protruding parts into the pockets. After this, assemble all 4 modules together.

14. The result is a geometric figure called an octahedron.

Before you begin, you need to prepare. For this you may find the following materials useful:

1. Preparation of a figure that needs to be transferred to the material for our figure.
2. Glue. It's best to use PVA - it dries long enough for you to correct mistakes when gluing.
3. Scissors.
4. Ruler.

Once you have obtained all the necessary components, you can begin work. Now we will present a diagram by which this figure can be made:

So, our figurine is ready and now you can start decorating it. It can be painted with paints or pencils, or hung on a string. Various sparkles and pieces of rain are also perfect. Very often, such a decoration can be used as a decoration for the New Year tree. Also, you can do a really fun thing using icosahedrons, namely a soccer ball, which is a truncated figure. If you examine it carefully, you will notice that it consists of twelve pentagons and twenty hexagons, which are of the same size. A painted figurine will look great, and different colors of simple elements will show the difference even more.

If this idea intrigues you, then below we present a development with which you can make a ball:

As you can see, creating paper figures is a very interesting process. Once you learn how to make an icosahedron, you can move on to other, more complex geometric shapes. This is especially useful for children who can develop spatial thinking, learn geometry and improve fine motor skills from an early age. If the child is very small, then the help of parents may be required, however, he will happily play with the finished toy on his own. Nevertheless, this activity will also be useful for adults - this is a great hobby that can help you relax or just pass the time. If you like work that is not painstaking and requires attention, then this activity is just what you need.