Bagatohedrons from cardboard. How to make an icosahedron from paper? Yak zrobiti zirchastiy bagatohedron from cardboard scheme
Making potions with your own hands is not only for children, but we have grown up. However, for the grown-ups, a sufficient number of models have been devised, which are folded over for an hour, stained on their creations. In the rest of the hour, grown-up children were interested in the creation of folding geometric shapes. Before such a type of figures lie an icosahedron, which is a regular bagatokutnik and є one of the Platonic solids - regular bagatohedrons. This figure has 20 tricot faces (equal-sided tricots), 30 ribs and 12 vertices, and 5 ribs. The correct icosahedron from the paper is easy to finish, ale cicavo. If you bury origami, then it’s not easy for you to create a paper icosahedron with your own hands. Yogo zrobiti from color, corrugated paper, foil, packing paper for tickets. Vykoristovuyuchi different materials, you can give more beauty and efficiency to your icosahedron. All lay only in the imagination of the creator and the handy material that is on the table.
We offer you a sprinkling of variants of the icosahedron roses, which can be developed, transferred to thin paper and cardboard, folded along the lines and glued.
How to create an icosahedron with paper: a diagram
In order to select the icosahedron from the arch to paper or cardboard, it is necessary to prepare the following materials in advance:
- icosahedron layout;
- PVA glue;
- scissors;
- line.
Under the hour of folding the icosahedron, it is important to pay special attention to the process of creasing all the details: in order to fold the papiers evenly, you can victorious the line.
Tsikavo, that the icosahedron can be used in everyday life. For example, in the form of a truncated icosahedron (a bagatahedron, which consists of 12 p'yatikutnikіv and 20 six-kutnikі in the correct form), the football ball is beaten. It is especially evident that it is rozfarbuvat іkosahedron, scho wiyshov, black-and-white color, like the ball itself.
Such a football ball can be made independently, having developed a slit of a truncated icosahedron in 2 examples:
The creation of the icosahedron with one's own hands represents the cicada process, which evokes thoughtfulness, patience, that great amount of paper. However, the result, taken away from the result, will be quiet for another hour. The icosahedron can be given to cherish the child, as if it had already reached the trinity age. Playing with such a folding geometric figure, we develop not only figurative thoughts, open spaces, but also know the light of geometry. Well, if a grown-up man has created an icosahedron independently, then such a creative process of constructing an icosahedron allows one to pass an hour, and also to boast before his close minds of creating folding figures.
There have already been published models of bagatohedrons, but I would like to add my own. Sent to yourself, on wenninger.narod.ru. I got a book on the spot, then, if I connected to the Internet, wrote a sheet to the author and otrimovid, then the book with a sheet was ruined, but I knew the site and continued the work of the model.
Yakshcho tsikavo, I can take a picture of the skin okremo.
Oleksandr
Well, for the hell of the working people, I'm posting a photo of all the rich granaries. I don’t particularly remember the name, I classify them according to the rich-faceted kutka. At the book (Wenninger. Models of bagatohedrons) there are chosen like bagatohedrons, so are their star parts of the form. Platonic body with 5 swollen regular bagatohedrons. They have faces of the same type (correct tricuts, squares and pentacles) and all richly shaped cuts are the same. Archimedes added 13 swollen napіvregular bagatohedrons (facets - different bagatokutniki, but all kuti, like before, however). And from the same brother, not poukli bagatokutniki (at the knizі vikoristovuyutsya trikutniki, squares, pyatikutniki, eight-kutniki and ten-kutniki), but their dawn forms (p'yatikutna, eight-kutna and ten-kutna zirka), then a mass of new bagatokutniki will come out. Before that, the edges can be folded in the same way as they look like stars, so non-puffy bagatohedrons can be folded like z zirchast bugatokutnikіv, so і z puffy.
Nareshti, similarly to the fact that the continuation of the line transforms the bulging horn into the mirror one, so the continuation of the faces establishes the star parts of the form. It is true that there are only 4 regular bagatokahedrons of this type (all three parts form a dodecahedron and one starry form of an ocahedron), in the other sides there are irregular bagatokutniks, or the bagatokutnik breaks into a sprat of okremy bagatokahedrons.
Particular beauty is given to forms, at which faces one can see from two sides, and also diri, which revenge, plus those, parts of them only hang one by one with peaks.
Obviously, bagatohedrons do their math, but let’s talk about it.
The photographs are accompanied by models of richly-faceted bushes. This is the base of the pyramid, like a weed, like a top of a bagatohedron, cut a small piece, like a cake. 3, 4, 5, 6, 8 and 10 designate opulences of bagatokutniki, 5/2, 8/3 and 10/3 - pyatikutnu, eight-kutnu and ten-kutna star (the sequence of peaks should be broken in two, 3 and 3 turns near the center).
Let's go. The back of the tricouts. (at the arms - model numbers from the book).
Infinite family of prisms.
Tricut prism.
Chererougіlna prism, hexahedron, cube (3).
P'yatikutna prism that її zіrchasta form.
Six-point prism.
Tetrahedron (1).
Dodecahedron (5) and three yogo starparts of the form, yakі є regular bagatohedrons: small dawn dodecahedron (20), great dodecahedron (21) and great round dodecahedron (22):
Shortening tetrahedron (6).
Shortening octahedron (7).
Shortening hexahedron (cube) (8).
Shortening of the icosahedron (9). Previously, football balls were sewn like this.
Shortening dodecahedron (10).
Rhomboid cuboctahedron (15).
The rhomboid icosododecahedron (16).
Quasi-expansion hexahedron (92).
Quasi-expansion cubooctahedron (93).
The great quasi-usualization of the icosododecahedron (unfortunately, in the middle of the German and once zlamavsya). (108)
Let's move on to rich-faceted faces, where 4 faces meet at the edge.
The back of the head is to stand at the sight of a square.
Infinite family of antiprisms.
Trikutna antiprism, octahedron (2), that її dawn form - dawn octahedron (19).
Square antiprism and її two parts of the form.
Cuboctahedron (11) and її zіrchastі form (43 - 46).
The icosododecahedron (12) and its її parts of the form (47, 63, 64), and the books of them are even richer.
The rhombicuboctahedron (13) is the same simple form.
І tse bagatohedron (pseudo-rhombicuboctahedron) having accumulated a lot of noise, because yoga was published less than 2000 years after Archimedes (at the turn of 50-60 r.r. of the 20th century). In fact, the new one has a defect: if I said that the right buget-faceted kuti (vertex model) is the same, then you can note that the order of bypassing the faces at the side vertices is always mirror-like, for example, in one of the vertices of the face there is a harazd. 4-4-4 behind the year's arrow, then at the sudny top of that very order, but the opposite year's arrow. So from, the pseudorhombicuboctahedron has pairs of vertices, which do not seem to have mirror symmetry.
Rhombicosidodecahedron (14).
Maliy ikosokosododecahedron (71).
Dodecodedecahedron (73).
Rhombicodecodecahedron (76).
Great icosododecahedron (94).
Great dodecoicosododecahedron (99).
Now bagatohedrons, for which those 4 faces converge in one vertex, but the order is crosswise:
Tetrahemihexahedron (67).
Octahemioctahedron (68).
Malium cubocuboctahedron (69).
Axis of a kіlka schemes, with which you can make volumes of geometric figures.
The simplest tetrahedron.
Trochs will be more foldable octahedron.
And the axis is a volume figure dodecahedron.
Another one - icosahedron.
You can look at the report about the preparation of all figures here.
The axis looks like this about the figures not in the chosen view:
And the axis looks like this is already ready:
From the large geometric shapes, you can create a lot of original designs, including packaging for a gift.
So that children remember better, they make geometric figures, and they knew how stinks are called, you can make cardboard out of thin paper volumetric geometric shapes. Before the speech, on the basis of them, you can prepare a garn of gift wrapping.
- solid paper, or cardboard (more colorful);
- line;
- olive;
- scissors;
- glue (preferably PVA).
Nayskladnіshe — tse rozrobiti and christened the rosary, you need basic knowledge of the armchair. You can take ready-made cutouts and send them to the printer.
Sob the line will die with a straight line and a gostroy, you can speed up with a dull bark and a metal line. Under the hour of the line, you need to bend your neck strongly at the bіk Rukh, practically putting it on.
Tse prosthesis of the trihedral pyramid
Tse riser cube
Tse rosette of the octahedron (chotyrihedral pyramid)
Tse riser of a dodecahedron
Tse rozgortka icosahedron
Axis here you can find patterns of folded figures (Platonic Tila, Archimedean Tila, bagatohedrons, polyhedrons, different kinds of pyramids and prisms, simple and slanting paper models).
Independently zmaistruvavshi z paperer about'mnі figures can vikoristovuvat їх for rozvagi, ale y navchannya.
For example, you can actually show the child how it looks like that chi іnsha to stand, give it to hold it in your hands.
Otherwise, it is possible, with the help of the method, to develop schemes with special designations.
So I pronounce below to know from this dodecahedron, Like a simple one, so with small little ones, like little ones to screw up the respect of a little one and teach him to make more fun and cheer.
Also the scheme Cuba you can vikoristovuvati for navchannya numbers.
Scheme pyramids you can help to learn the formulas that can be seen to the figure figure.
In addition, I propon you to familiarize yourself with the scheme octahedron.
Scheme tetrahedron so dopomozhe vivchiti kolori.
As you have understood, made more patterns, it is necessary to expand, bend, bend along the lines, glue along special narrow ties that fit to the opposite sides.
The first step is to begin to work about the geometric figures, it is necessary to show (because you know, as if looking) the figure in the 3D world: the number of faces can be that chi іnsha figure.
The back of the head needs to be correctly placed on the paper, the figure on the edge, so that you can join yourself together. The facets of the skin figure have a simple shape: a square, a three-cut, a rectangle, a rhombus, a six-cut, a thin kolo.
It is even more important that the length of the ribs of the figure, as if they will be joined one by one, small the same length, so that the hour of the day will not cause problems. As the figure is folded from the same faces, I used to propagate the pattern for the first hour of the chair to beat the pattern. You can also get ready-made templates from the Internet, design them, bend them with lines and stitches (glue).
Pyramid - rosemary. Pyramid strip for gluing. Rosgortki with paper
Rectangle, square, tricutnik, trapezium and others - geometric shapes of exact science. Pyramida is a bagatohedron. Supporting the tsієї figure is a bagatokutnik, and the bіchny faces of the tricutnik, which can make a folded top, or a trapezium. For a complete presentation, that development of any geometric object is preparing layouts. Vicorist is the most manipulative material, for which the pyramid is victorious. The top of the richly-faceted figure, splayed on the flat, is called the rosary. Create a layout to help the method of converting flat objects into volumes of bagatohedrons and knowledge of geometry. It is not easy to make paper cuts from paper and cardboard. It is necessary to win the armchair for the assignments of measurements.
Materials and attachments
Modeling and vikonannya rich-faceted volumetric geometric figures - tsіkavy and hoary process. From paper you can vikonat a large number of layouts. For work will be necessary:
Designation of parameters
We are significant, what will be the pyramid. The cut of this figure is the basis for the preparation of a volumetric figure. Vikonannya work and vimagatime boundary accuracy. It will be impossible to pick up a geometric figure for an incorrect chair. It is permissible, it is necessary to prepare a layout of the correct tricot pyramid.
Be-like a geometric body may be songs of power. The figure is given as the basis of the correct bagatokutnik, and the top is designed to the yogo center. As a base, a equilateral tricot was chosen. Tsya umova spelled out the name. The bichni ribs at the pyramid are tse tricutniks, a lot of which can be found in the bagatohedron chosen for the base. Times will have three. It is also important to know the expansion of all storage parts, from which the pyramid will be stored. Rosgortki with paper are folded in the same way to all data of the geometric figure. The parameters of the future model are set in advance. Vіd tsih danih to lay down the vicarious material.
How do you win the rosette of the right pyramid?
The basis of the model is arch paper and cardboard. The work is being repaired from the chair of the pyramid. The figure is presented to a roaring look. The flat image on the paper shows the distance to choose the size and parameters. A correct pyramid is the basis of a correct bagatokutnik, and the height passes through the yoga center. We prepare a simple model. I have a tse trikutna pyramid. It is important to expand the chosen figure.
Folding layout
Virіzaemo with scissors vykonaniya little babies behind the contour. Gently fold the cut along all lines. The trapezoid valves are filled in the middle of the figure in such a way that its edges are closed. Їx smeared with glue. After thirty minutes, the glue will dry. Volumetric figure is ready.
Rosgortka chotiricutnoy pyramid
The back of the head is visible, as if looking like a geometric figure, the layout is being prepared. Supporting the formed pyramid є chotirikutnik. Bichni ribs - tricouts. For robotic work, the same materials and attachments, which are in the front version. The armchair is embroidered on paper with an olive. At the center of the sheet there is an armchair with a choice of parameters.
Skin side of the foundation dilimo navpil. We draw a perpendicular, which will be the height of the tricot facet. The design of the compass, which is the most beautiful old face of the pyramid, is worked on the perpendiculars of the notch, placing the foot at the top of the base. Having offended one side of the base, it is back with a taken point on the perpendicular. As a result, a square is taken in the center of the armchair, on the edges of a kind of embroidered tricot. To fix the model on the side faces, to make additional valves. For supple reinforcement, a centimeter-wide coat is sufficient. The pyramid is ready before picking.
The final stage of the layout
I will take the shape of the figure and see it along the contour. On the baptized lines, papiers are made. The choice of ob'єmnoї figures shattered with a path of gluing. Transferred valves and lubricated with glue and fixed the model.
Volume models of folding figures
After the completion of a simple model of a bagatohedron, one can proceed to folding geometric figures. The burning of the truncated pyramid is richly folded at the vikonanna. Її basics є similar bagatohedrons. Bichni faces - trapeziums. The sequence of vikonanny roboti will be the same, like the one in which a simple pyramid was prepared. The riser will be more bulky. For vikonannya armchair vicorist olive, compasses and line.
Pobudov chair
The burning of the pyramid of the sacked is vikonuetsya in a sprat of stages. The beaded facet of the truncated pyramid is a trapezium, and the bases are also bagatohedrons. Let's say that are squares. On the archway, the paper is embroidered with armchairs of a trapezium from the given dimensions. The bichni sides of the trimmed figure are continued to the peretina. As a result, equilateral tricot is taken. Yogo bek vimiryuemo with a compass. On an okremy arch, the paper will be a ring, the radius of which will be a death.
The next stage is the appearance of the bichnyh ribs, as if the pyramid was stubborn. Rozgortka vykonuєtsya in the middle of the painted stake. Compasses win the lower base of the trapezium. If five points are indicated, then the lines should be connected from the center. We take away chotiri of equal-femoral tricots. Compasses vimiryuєmo bіk trapezії, painted on the cream arch. Tsya v_dstan' v_dkladaєmo on the skin side of the painted knitwear. Take the points back. The bichni faces of the trapezium are ready. It is only left to paint the upper and lower bases of the pyramid. In this vipadku, tse bagatohedrons are squares. Up to the upper and lower foundations of the first trapezium, there are domaly squares. On the armchair there are images of the moustache, like a maє pyramid. Rozgorka is practically ready. There are no more homemade back valves on the sides of the smaller square and one on the sides of the trapezium.
Completed modeling
Before gluing the bulky figures of the armchair along the contour, they are cut with scissors. They gave the rosette to carefully bend behind the crossed lines. Creeper valves are filled in the middle of the model. It is smeared with glue and pressed to the edges of the pyramid. Let the models dry.
Preparation of different models of bagatohedrons
Vikonannya ob'єmnih models of geometric figures - tsіkave busy. In order to thoroughly master yoga, you should start with the simplest roses. Proceeding step by step from simple designs to folding models, you can proceed to the creation of the most sophisticated designs.
Roots of geometric shapes
Great selection of roses of simple geometric shapes.
The first acquaintance of children with paper modellings always starts with simple geometric figures, such as a cube and a pyramid. It’s not for rich people to go out to glue a cube the first time, sometimes it takes a few days to build a truly equal and unworkable cube. Larger foldable figures of a cylinder and a cone wiggle at the kіlka more zusil, lower a simple cube. If you can’t carefully glue geometric shapes, it means that it’s too early for you to take care of folding models. Take care of yourself and teach your children to the client and “azi” modeling for ready-made roses.
For the cob, I, obviously, teach you how to glue the greatest cube. The cuticles are cut for two cubes, a big one and a small one. A larger folding figure is a small cube, to which it is more foldable, lower is great.
So let's do it! Zavantzhte rosettes of all figures on five arches and instruct on the opening paper. Before that, how to draw that glue of geometric figures on obov'yazkovo, learn this article about how to choose paper and how to correctly bend, bend and glue paper.
For more lucid friend raja, you can twist the AutoCAD program and I give you the layouts for this program, and also read how to rozdrukow the AutoCAD. Cut the rows of cubes from the first sheet, along the lines of the fold of the obov'yazkovo, draw a bare compass under the liner, so that the papier is well folded. Now you can fix the glue cubes.
To save paper and for any kind of fire, I've made a sprat of small cubes, so that you don't want to glue more than one cube, otherwise you won't see it the first time. One more clumsy figure - the pyramid, you will know the rosettes on the other arch. Similar pyramids were crafted by ancient Egyptians, though not with paper and not such small roses.
And the same pyramid, only on the front in the front are not chotiri, but three faces.
Trihedral pyramid rosettes on the first arch for a friend.
І one more comedy pyramid with five sides, її ruffles on the 4th leaf of a visible star in two primaries.
More foldable figure is the pentahedron, if you want the pentahedron to be folded more folded, glued lower.
Rosgorki pentahedron on another arch.
Axis mi th distanced folding figures. Now it’s not easy to get stuck, it’s not easy to stick together like this! On the back of the head is a prominent cylinder, yogo rosettes on the other arch.
І tse folding to stand against the cylinder, tk. її pedestal has not a colo, but an oval.
Rosgortki tsієї figures on another arch, for the oval base, two spare parts were cut.
To carefully select the cylinder and yoga parts, it is necessary to stick to the stick. From one side the bottom can be glued without problems, just put the glued tube on the steel in front, put a circle on the bottom and fill it with glue in the middle. Keep in mind that the diameter of the pipe and the round bottom fit snugly one to one, without gaps, otherwise the glue leaks and everything sticks to the table. Glue the other edge more foldably, then glue additional rectangles in the middle of the paper at the edge of the pipe. Qi rectangles will not let the foundation fall, now you can glue the circle to the beast without any problems.
A cylinder with an oval base can be glued the same way as a great cylinder, but if it has a smaller height, then it’s easier to insert an accordion in the middle of paper, and lay a base on top of a friend and glue it along the edge with glue.
Now it’s more foldable to stand - a cone. Yogo details on the third archway, a spare circle for the bottom on the 4th archway. All the folding of the cone is glued to its hot top, and then it will be even more folding to glue the bottom.
The figure of the head is foldable and at the same time simple. The sack is made up of 12 pentahedrons, the swells of the kuli are on the 4th sheet. The two halves of the sack are glued on the back, and then the insults are glued together.
To finish the tsіkava to post - a rhombus, її details to the third sheet.
And now the two are even more similar, but with the same different figures, now the vibrancy is only in the base.
If you stick together these offensive figures, you won’t understand what you’ve got in such a way, the stench seemed to be unacceptable.
One more cicava figurine - tse tor, only vin we have more forgiveness, yogo details on the 5th arch.
I’m on the verge, stay to post from the equal-sided tricks, I don’t know how to call it, but to post is similar to the star. Rosgortki ts_єї figures on the fifth arch.
That's all for today! I wish you success in your hard work!
COMMENTS
Set by geometry: tetrahedron, cube, octahedron, dodecahedron, icosahedron. The tetrahedron, the cube and the dodecahedron were broken, and the axis was two, which were left behind (((
More blamed the difficulties of gluing.
dyakuyu, xs che b robiv yakbi not the whole site =)
Thank you very much!)))) they already lied!
I wouldn't have been able to do that, I would have known it well.
to help, as if to build a rosette of the Chotiricut pyramid with a base.
How do you build the torus of a torus (tobto kіltsya, vіrnіshe, yogo surface)?
The food is given with a practical method, I want to independently sheathe the kermo machine with a sheet, but for this it is necessary to create a shape, the axis here and vinyl is difficult - do not show all the paint, even if the surface of the torus is t.z. the surface does not grow up (virnishe, mentally-goes up).
People, help with joy or help, please!
I would have pleased you to go to the store and wonder how to sew similar covers for car kerm. A specific material has been lifted, with it you can work practically everything, you can’t do this with a paper, it’s important to make it here, rather marvel at how it’s already broken and at home think about how you build your own.
how to build a shortened pyramid
Thanks for the information, but not all figures are shown. We went to the 9th grade, but not in Russia. Help needed. Good luck, Tamara.
Maybe a bad diet, but how about zrobity from a paper bag? tobto. not just a colo, but the volume of the sack itself? what is it that has risen in nature is such a splinter?
Rosgortka kuli z paperu ¾ parts, females of paperu, which sound along the edges. Rosgortka kuli is similar to the little ones from the husband on the kavun.
Dmitre, I also remember from the course of school geography 🙂
And the axis is like a zrobiti from the atlas in the electronic view of the cool in the electronic view, so that we can later develop and paste it?
Why parameters are not specified? Length, width, etc.?
how to make a cylinder with paper help plz
Great people DYAKUЄ.
Wirobi with children. SOCCER BALL AND POLYHEDRALS FROM A QUIT PAPER.In the midst of my readers, there are a lot of children's kindergartens and kerrivniks of Artistic groups, at the link with zim I publish posts with virobs at once with children and for children.
Before we speak, I would like to recommend to all the fathers a very good child studio "Teremok", as it has already proven itself to be one of the best studios for the spiritual and lighting robots with children. "Teremok" will help your little one to know the language of splintering with one-year-olds, rozvin povat to the elders, rozvezhivat, vlashtovuchi holy that competition and richly іnshoy. It is also necessary, for children, from an early age, to pinch love to creativity. Tse viroblya stink dopitlivist, expand svetoglyad, pinch love to practice. The studio has a good artistic group of different types and genres of figurative art. You can learn more about the studio on the website - http://teremok64.ru.
And now, p redagu to you to take on children and grow together with them bagatohedrons from a colored paper. Tse not only zahopit їh, stench otrimayut first knowledge of mathematics. Below there are five templates on deaks of bagatokutniks, yakі need to rozdrukuvat and zbіshiti. Everything is easy and simple, fold, bend and glue. Even more beautiful is the garland, yaskrava, that sleepy one is cheerful)
You can create a mockup of a soccer ball. For this one, bazhano, take a paper - more.
In the insert, the template of the ball in full size is folded from eight sides.
Attachment:
DODECAEDR
ICOSAEDR
octahedron
TETRAHEDRA
View templates and bend along the dotted lines
VOILA. You can pick them up on a thread and make a mathematical garland)
One of the simplest paper cuts is the dodecahedron-origami. Ale does not mean that the wine does not look defective, especially if there is a dawning difference. A decorative bagatohedron, similar to its other relatives - kusuds, is perfectly suitable for Christmas decoration, or as an original gift. The mini-dodecahedron can be twisted like a fashionable embellishment, making earrings or a pendant out of them.
Openwork model
Use a small sample of origami-dodecahedron types, but make it easier to understand the design of paper modules. A good task for children, as they need to learn the basics of space geometry and grown-ups, as they joke about effective benefits for relieving stress. Bazhano vikoristovuvati paprikas with a little one for a toy, you will give a special charm and color.
Pokrokov's instruction:
- For the creation of pieces, 30 of the same modules are needed. They are folded from rectangles, so that the spіvvіdnoshnja sides 3:4 can be made. For example, rosemary 6x8 cm, 9x12 cm thin. You can take both one- and two-sided leaves.
- Folding a leather rectangle navpil uzdovzh dovgoї side. For what reason Z-like zgin works.
- Roztashovuemo the husband, who has left, with her long side to herself. We bend the lower right corner uphill. I can turn it over 180 °. I repeat the action for the right lower kut (insh).
- Fold the figure diagonally, as shown in fig.
- Modules for the dodecahedron-cousids are ready.
Learn to eat them at the expanse of composition. For this, a short part of one module is inserted up to the “gut” of the second part of the other. And maybe so, so that the internal cuts and edges of both elements were bent.
Similarly, the third module is added, connecting it with the front two and forming a stable structural vuzol.
We keep the details one to one, the docks do not see a volume figure.
A stylish piece of decor emerges behind the rahunok of an inimitable paper with a print. So that the kusudama does not fall apart, it’s better to put together knotted elements for additional glue.
A detailed selection of the openwork dodecahedron is presented in the video-MK:
Kusudama from the correct p'yatikutniks
The scheme of folding the dodecahedron-origami with pentagons - equilateral p'yatikutniks, was developed by the American designer David Bril. For modules in vikoristovu 12 arches in A6 format, tobto 105x148 cm.
Pokrokov's instruction:
- The lateral straight-line folded at the later and transverse straight lines, hinting at the middle axis.
- The upper right and lower left corner bends to the center. We take away our kind of envelope.
- Similarly, we fold the protilezhnі kuti.
- I’ll prepare the five yards, “curve” the beast down the “valley”.
- The upper kut is lowered down and turned back. On the cross line of the line, which has appeared, from the vertical line of the figure, a dot is established. Before her, according to the devil's sake, we'll find out the best kuti.
- The pentagon module is ready. The remaining two bends are curved - there will be details of the fastening of the elements between themselves.
- Bіchni "vushka" one of the details is inserted into the "intestine" inshoy. Mіstsya z'єdnannya for naіynostі fix with glue.
- We continue to select until all 12 modules have been selected.
Of such dodecahedrons, the calendars on the floor are often broken. There are bumps on the skin edge. You can download the official handouts with the dates and days of the week from the Internet and stick them on the walls of the model. Viide is not only beautiful, but also practical.
Dodecahedron-zirka
The correct star parts of the bagatohedrons rise to the most beautiful geometric figures. From the moment of their appearance at the XVI century, the stench was vowed as a symbol of the perfection of the All-world. The small star dodecahedron was first inspired by the German astronomer and mathematician Johannes Kepler, the creator of the famous theory about the future Sonyach system. Bagatohedron may be well named: Arur Keli, in honor of the English scientist, who has made a majestic contribution to the development of linear algebra.
Maliy dawning dodecahedron-origami with a figure of 12 faces-pentagrams, with five pentagrams, which converge to the peaks. The wines are made up of 30 modules, which are made up of squares, with a size of 8x8 cm.
The correct bagatohedrons from long ago suffocated the people and served as a prototype of the world order. As it appeared, so it was not unbelievable. In 2003, while analyzing the data of the previous WMAP apparatus, launched by NASA for the development of background space vibrations, they put forward a hypothesis about the dodecahedral future of the All-World behind the principle of the Poincaré sphere.
Shchos similarly conveyed to the one who is alive in the V century. to the sound e. ancient Greek philosopher Plato. In his opinion about the classical elements of wines, he called the dodecahedron "a vivid divine arrangement of the Cosmos." All five of the correct bagatohedrons were called Platonic solids, in the name of the thinker, having first inspired a picture of light-budding for an additional reading.
The Pentagon, which underlies the dodecahedron, prompts on the principles of the "golden cut". This proportion, like the ancient Greeks respected "divine", is often measured in nature. Tsіkavo, scho spіvvіdnoshennia “golden perіzіzu” pritamanni only dodecahedron and icosahedron, three of the other Platonic solids have none.
Ancient Roman toys
On the territories of Europe, where the Roman Empire lay, there are still mysterious bronze figures in the form of a dodecahedron. The objects are hollow, with round openings on the skin side and bags that signify peaks. So far, scientists have not been able to unambiguously determine the function of these objects. It was deeply respected that these were their own toys, they later brought them to the objects of worship, which symbolize the All-Sveta of Budov. Abo the Earth, zgіdno s theory, which is consequently hung from the 19th century by light physicists, including Russian ones.
First, the French mathematician Poincaré and the geologist de Bemont spoke about those that our planet is a crystal of dodecahedral form. The stench was hardening, like the earth's crust, a football ball is dumb, it is formed from 12 regular pendulums, at the places of the formation of which anomalous zones and planetary force fields are scattered.
In the 1920s, the Russian physicist Stepan Kislitsin came up with the idea of French colleagues. Vіn pіshov dalі, declaring that the planet is not left in a stable state, on growth, from the dodecahedron step by step transforming into the icosahedron. Having explored the models of similar changes, recognizing the knots of a gigantic crystalline network, de, on one thought, the genera of brown copalins were sorted out: vugillya, naphtha, thin gas. In 1928, roci Kislitsin, spiraling on its research, showed 12 diamond-bearing centers on the surface of the earth, out of which 7 dos are in active exploration.
The ideas of a crystalline future of the planet continue to develop in the 21st century. It is clear to the rest of the hypothesis that the structure of power is similar to all living organisms, like space bodies, and human beings. Tim tsіkavіshe will choose the dodecahedron-origami, making his accountable to the great mysteries of the All-world.