Octahedron development for gluing. How to make an octahedron out of paper (video, photo)? Sketch is a faithful assistant

An octahedron is a polyhedron that has triangles as faces and is a regular polyhedron. So it has only eight faces and, accordingly, twelve edges, six vertices.

It looks like this:

To make it, draw it like this on cardboard:



Wrap the specially left edges inside and glue them together.

An octahedron is a geometric figure that has eight faces. Each face is an equilateral triangle.. In order to make this figure, you need to draw the following figure of triangles on cardboard (or paper):



Or these:





Fold along the lines and assemble the shape, glue the sides.

The end result should be a figure like this:



An octahedron is a polyhedron with triangle faces, its type is a regular polyhedron, there are 8 faces, 12 edges, 6 vertices, and 4 faces at a vertex. This is not such a simple cubic polyhedron, but it is easy to make. Watch the video







An octahedron is such a three-dimensional figure, it is not at all difficult to assemble it from paper, you only need paper, scissors and glue. You can draw the pattern yourself, or you can print it from the Internet.



You can also assemble it using a video, for example, this one, which shows the process of applying the pattern.

• Making an octahedron out of paper

  First you need to make a pattern, from which we will then fold and glue the octahedron. In principle, an octahedron can be made by simply gluing two pyramids together, but there is an even simpler way, that is, you can make it from one sheet of paper.

  The following octahedron pattern is popular:

  

  When you have drawn a pattern (although it is better to take a ready-made one on the Internet and print it out on a printer), cut it out. Then we bend the figure along the fold lines, that is, we try to figure out what to attach to what in order to assemble an octahedron from the pattern. Next, we coat the glue fields (small stripes along the edges of some sides) and connect the sides of the octahedron to each other.

  Then we hold it in our hands a little (we press it) until the glue dries sufficiently, that is, until the moment when the figure is held on its own by the glue. It is best to use glue Supermoment, then everything will work out quickly and firmly.

The octahedron has 8 faces, all of them triangular, so assemble this option volumetric figure is not difficult. You can even draw the so-called pattern yourself. In order not to make a mistake, it is better to take a squared piece of paper and draw a figure like this on it, transfer it to thick paper and even write something on future edges, for example, like this:



Well, then compare all the edges and glue them together.

If we are talking about a regular octahedron, then the process is quite simple. It is enough to print and cut out the pattern - the layout offered here, or you can draw it yourself, looking at the photo, because the octahedron pattern is six equilateral triangles in a row with valves and two on the sides (you can say opposite each other, but here it is important at what angle look) without valves.



This video clearly shows the manufacturing process octahedron: bend all the lines, coat the valves with glue and attach the sides to the valves, it is impossible to make a mistake in the sequence of actions:

But here the figure is more complicated - stellated octahedron. The craftsman shows how such a complex polyhedron can be made from one sheet of paper without glue. He also gave a step-by-step explanation of his actions. Let me note right away: it’s easier to watch them than to try to do it yourself, at least the first time.

The exact same process, but with a different master, with different hands and comments, can be seen here:

As an option: process of creating a stellated octahedron - puzzles explain (and also provide layouts) here.

Which appeared in ancient times, one of the most interesting is the octahedron. This figure is one of the five solids called Platonic solids. It is regular, symmetrical and multifaceted, and also has a sacred meaning in terms of stereometry, practiced in Ancient Greece. Today, this geometric body is studied by children at school, and in order to understand its structure better, we will look at how to make an octahedron from paper.

Let's prepare materials

All that is needed during this process is scissors, glue, a pencil, a ruler, and the paper itself, which will form the basis of the future craft. It is believed that the independent production of such stereometric figures improves abstract thinking and allows for better orientation in space. Therefore, with the help of our short lesson, you can catch up on the geometric skills you missed at school, or invite your child to create something similar if he has problems with the perception of geometric spaces and figures.

Sketch is a faithful assistant

The first option on how to make an octahedron out of paper is a ready-made sketch. The article offers a picture that shows this figure in a scan, and all that remains for you is to print it and glue it along the outlined lines. This way your craft will have the most accurate parameters. Just remember to glue the paper onto the cardboard first so that the octahedron is more durable and lasts longer. This is especially important if it is intended for a child.

Everything with your own hands

Another option for making an octahedron out of paper is based on simple formulas and drawing. This geometric figure consists of 8 faces, 6 vertices and 12 edges, each 4 of which converge at one vertex. If you add up all the angles of the octahedron into a single number, the sum will be equal to 240 degrees. It is also worth noting that this mythical stereo figure has a triangular base and is completely symmetrical, which is why it is often called an antiprism.

Stereometry lessons

The development of the octahedron represents a certain set of triangles that are completely equal to each other. Six of them are lined up in a single row according to the “jack” principle, and the other two with their bases are adjacent to the two middle figures from different sides. Therefore, the answer to the question of how to make an octahedron from paper without layouts is simple. You just need to choose a single face size and base it on eight equilateral triangles. Just remember to leave allowances on the fold line along which you will glue the future craft.

Intricate mysteries of geometry

There are various varieties of such a stereo figure. Among these is the cuboctahedron. The development consists of 6 squares and 8 regular triangles, which are assembled into a three-dimensional body according to the rules of symmetry. This figure is semi-regular, and, it is worth noting, quite young. It was discovered by the creator Leonardo da Vinci, and was then called the “stellated octahedron”. You can also do it according to the scheme proposed in the article.

Which appeared in ancient times, one of the most interesting is the octahedron. This figure is one of the five solids called Platonic solids. It is regular, symmetrical and multifaceted, and also has a sacred meaning in terms of stereometry, practiced in Ancient Greece. Today, this geometric body is studied by children at school, and in order to understand its structure better, we will look at how to make an octahedron from paper.

Let's prepare materials

All that is needed during this process is scissors, a ruler, and the paper itself, which will form the basis of the future craft. It is believed that the independent production of such stereometric figures improves one's ability to orientate oneself in space. Therefore, with the help of our short lesson, you can catch up on the geometric skills you missed at school, or invite your child to create something similar if he has problems with the perception of geometric spaces and figures.

Sketch is a faithful assistant

The first option on how to make an octahedron out of paper is a ready-made sketch. The article offers a picture that shows this figure in a scan, and all that remains for you is to print it and glue it along the outlined lines. This way your craft will have the most accurate parameters. Just remember to glue the paper onto the cardboard first so that the octahedron is more durable and lasts longer. This is especially important if it is intended for a child.

Everything with your own hands

Another option for making an octahedron out of paper is based on simple formulas and drawing. This geometric figure consists of 8 faces, 6 vertices and 12 edges, each 4 of which converge at one vertex. If you add up all the angles of the octahedron into a single number, the sum will be equal to 240 degrees. It is also worth noting that this mythical stereo figure has a triangular base and is completely symmetrical, which is why it is often called an antiprism.

Stereometry lessons

The development of the octahedron represents a certain set of triangles that are completely equal to each other. Six of them are lined up in a single row according to the “jack” principle, and the other two with their bases are adjacent to the two middle figures from different sides. Therefore, the answer to the question of how to make an octahedron from paper without layouts is simple. You just need to choose a single edge size and base it on eight. Just remember to leave allowances on the fold line along which you will glue the future craft.

Intricate mysteries of geometry

There are various varieties of such a stereo figure. Among these is the cuboctahedron. The development consists of 6 squares and 8 regular triangles, which are assembled into a three-dimensional body according to the rules of symmetry. This figure is semi-regular, and, it is worth noting, quite young. It was discovered by the creator Leonardo da Vinci, and was then called the “stellated octahedron”. You can also do it according to the scheme proposed in the article.

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 execution 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. Regular icosahedron It is quite difficult to assemble from paper, 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, 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 reverse Special attention on 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 large quantity 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 get 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.

Positive polyhedra were famous back in Ancient Greece. They are called "Platonic" solids. The four positive polyhedra are the tetrahedron, icosahedron, cube and octahedron- personify the four “essences”, the elements. The octahedron symbolizes air.

You will need

• - paper;
• - pencil;
• - ruler.

Instructions

1. The octahedron consists of eight faces, which are positive triangles. In a right triangle, all sides are equal to each other. The angles between the sides of such a triangle are 60°. The heights, medians, and bisectors are the same. To build the right octahedron and you will need a cube.

2. To construct a cube, draw a square. Step back some distance to the right and up, build another similar square (the left and bottom lines will be dotted). Combine the corresponding paired points of both squares to visualize a cube. From the fact that on its basis you will build octahedron, make it huge and distinct.

3. Let a cube be given. Need to build octahedron, inscribed in it. Draw diagonals for the entire face of the cube. Mark the intersection points of the diagonals. Connect all the resulting points with each other. Positive octahedron, inscribed in a cube, ready.

4. To prove that the resulting figure is positive octahedron, you need to confirm the correctness of the triangles. To confirm that the face triangles are correct, draw perpendiculars from their vertices to the edges of the cube. Use the properties of right triangles and cubes.

5. It is also allowed to build octahedron, described around a given cube. Let a be the length of the edge of the cube. Find the centers of the entire face (these are the intersection points of the diagonals). Draw straight lines through the centers of opposite faces. They will intersect in the center of the cube, which can be designated as point O.

6. It turns out that there are two lines intersecting at point O. Set aside a segment equal to 3a/2 on each of the lines on both sides. Combine the ends of the segments you received. This will be the framework of the positive octahedron a, described about the cube.

By medians of a triangle we mean segments that are drawn from the corresponding vertices of the triangle to opposite sides and divide them into 2 equal parts. In order to build medians in a triangle, you need to take 2 steps.

You will need

• -Pre-drawn triangle, side sizes are arbitrary;
• -Ruler;
• -Pencil and pen.

Instructions

1. Take a pencil and a ruler, and then, with their support, points are marked on the sides of the triangle so that they divide the corresponding sides of the triangle in half. One of the options for how they should be noted is in Figure 1.

2. Now, with the help of a red/blue or other colored pen and ruler, a segment is drawn from each vertex of the triangle, and in such a way that it connects the vertices of the triangle with their corresponding opposite straight lines at the points that were erected in the first step. An approximate version of how this should turn out is shown in Figure 2.

Video on the topic

Note!
In order to check the correctness of the construction, you need to take into account that all the medians of the triangle intersect at one point, which is called the center point.

If you have a sauna on your property, know that it is not an easy sanitary and hygienic room. This is a real home hospital. In the steam room, your skin is cleansed, everything unnecessary is removed from the body, irritation and fatigue leave it. What massage compares to a birch broom? It was decided that it was necessary to build steam room !

Instructions

1. Building a bathhouse with a hefty steam room is not an easy task. Firstly, the building site must meet every fire safety requirement, because a sauna is an object of increased fire hazard. It is for this reason that even in ancient times, bathhouses in Rus' were built away from housing, in vegetable gardens, to protect rivers and reservoirs. Secondly, not just any tree is suitable for building a steam room. Before construction begins, you need to select the necessary material. Thirdly, decide on the design of the stove, which will provide the heat and steam needed for the steam room in the required quantity.

2. It turns out that the site for construction has been chosen, and the location of a nearby water source has been taken into account. Place the bathhouse in a picturesque corner of your site. For a log house steam room, timber made of coniferous wood is best suited. As a vapor barrier, use aluminum foil placed on the inside of the steam room walls. In this case, two problems go away - the foreign smell from the sealing material, the one that was used when laying the timber (tow, rope, etc.), disappears; and, in addition, you will get rid of the origin of the resin on the walls. Cover the ceiling and walls on top of the vapor barrier with a board made of aspen or alder. These types of wood make the air in the steam room “lighter”.

3. The best wood for making shelves is linden. Any board other than birch or coniferous will be suitable for the floor. The first one does not work well in conditions of high humidity (it quickly rots), the second one releases resin when heated, which causes some inconvenience. The shelves are made on different tiers. This is necessary so that when you log into steam room, could first warm up and get used to its warmth by sitting on the lower shelf. And after that it’s great to take a steam bath on the top shelf. Their dimensions must be such that you can comfortably sit on them while lying down.

4. And finally, the heart of the steam room is the stove. The easiest and by far not the worst option is a standard metal stove. It uses firewood as fuel. Make the firebox with an exit to the dressing room. This will allow you, without making additional devices, to provide it with heat (heat will come from the front wall of the stove) and any debris (wood chips, etc.) will be located outside the washing and steam compartment. Isolate the stove outlet from the wall, covering it with bricks. Also line the stove inside the steam room with red brick. The distance between the walls of the oven and the brickwork should be within 2-3cm. The gap is needed so that the oven, expanding when heated, cannot break the brickwork. Lining the furnace with bricks is necessary in order to smooth out the steep temperature of the metal, and heated bricks retain the heat received from the iron longer.

Video on the topic

The octahedron is one of the four positive polyhedra, to which people attached magical significance 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, each of which is an equilateral triangle. In geometry, an octahedron is traditionally 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 regular triangle in which all sides are equal and each angle is 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. The correct triangles will come out 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
Wire for similar models must be chosen that will hold 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.

Helpful advice
Lines that are not visible must be dotted. If you doubt whether one or another segment is visible, it is better to build a dotted one. It is easier to complete a dotted line to a solid strip than to correct a solid line to a dotted line.