A lot of interesting things can be found for yourself in those areas of science that, it would seem, will never be useful in the usual life of a simple layman. For example, geometry, which most people forget about as soon as they cross the threshold of school. But in a strange way, unfamiliar areas of science become very exciting when you encounter them closer. So the geometric development of the polyhedron - a thing completely unnecessary in everyday life - can be the beginning of an exciting creativity that can capture both children and adults.
Beautiful geometry
Decorating the interior of the house, creating unusual, stylish things with your own hands, is a fascinating art. Making various polyhedrons yourself from thick paper means creating unique things that can become just an occupation for a day or two, or can turn into designer interior decorations. In addition, with the development of technology capable of spatial modeling of all kinds of things, it became possible to create stylish and modern 3D models. There are masters whousing the construction of sweeps according to the laws of geometry, models of animals and various objects are made of paper. But this is a rather complex mathematical and drawing work. To start working in a similar technique, the development of a polyhedron will help.
Different faces - different shapes
Polyhedra are a special area of geometry. They are simple - for example, blocks with which children play from an early age - and there are very, very complex ones. Building a sweep of polyhedra for gluing is considered a rather complicated area of design and creativity: you need not only to know the basics of drawing, the geometric features of space, but also to have a spatial imagination that allows you to evaluate the correctness of the solution at the design stage. But fantasy alone is not enough. To make scans of polyhedra out of paper, it is not enough just to imagine how the work should look in the end. You need to be able to correctly calculate it, design it, and also correctly draw it.
The very first polyhedron is a cube
Most likely, every person who attended school, even in the primary grades, encountered work in labor lessons, the result of which was supposed to be a paper cube. Most often, the teacher handed out blanks - a development of a cube polyhedron on thick paper with special pockets designed to glue the faces of the model into a single whole. Primary school students could be proud of such work, because with the help ofpaper, scissors, glue and their efforts turned out to be an interesting craft - a three-dimensional cube.
Entertaining edges
Surprisingly, a lot of knowledge about the world around us becomes interesting not at school, but only when you can find something fascinating in it that can give something new, unusual in everyday life. Not many adults remember that the same polyhedra are divided into a huge number of species and subspecies. For example, there are so-called Platonic solids - convex polyhedra, consisting only of regular polygons. There are only five such bodies: tetrahedron, octahedron, hexahedron (cube), icosahedron, dodecahedron. They are convex figures without depressions. Star polyhedra are made up of these basic shapes in various configurations. That is why the development of a simple polyhedron allows you to draw, or rather draw, and then glue a star polyhedron out of paper.
Regular and irregular star polyhedra
By folding the Platonic solids together in a certain order, you can build a lot of stellate polyhedrons - beautiful, complex, multicomponent. But they will be called "irregular stellated polyhedra". There are only four regular stellated polyhedra: the small stellated dodecahedron, the great stellated dodecahedron, the great dodecahedron, and the great icosahedron. Polyhedral nets for gluing will not be simple drawings. They, like the figures, will consistfrom several components. So, for example, a small stellated dodecahedron is built from 12 pentagonal isosceles pyramids, folded like a regular dodecahedron. That is, to begin with, you will have to draw and glue 12 identical pieces of regular pyramids, consisting of 5 equal faces. And only then can a star-shaped polyhedron be formed from them. Reaming the smallest star-shaped dodecaer is a complex and almost impossible task. To build it, you need to be able to fit on the same plane 13 scans of different geometric volumetric bodies connected to each other.
Beauty lies in simplicity
All volumetric bodies built according to the laws of geometry will look fascinating, including the star-shaped polyhedron. The development of each element of any such body must be performed as accurately as possible. And even the simplest volumetric polyhedra, starting with the Platonic tetrahedron, are the amazing beauty of the harmony of the universe and human labor embodied in a paper model. Here, for example, the most versatile of the Platonic convex polyhedra is the dodecahedron. This geometric figure has 12 absolutely identical faces, 30 edges and 12 vertices. In order to unfold regular polyhedra for gluing, you need to apply maximum accuracy and care. And the larger the figure in size, the more accurate all measurements should be.
How to build a sweep yourself?
Perhaps, in addition to gluing a polyhedron - at least star-shaped, at leastPlatonic, it is even more interesting to build a development of the future model on your own, evaluating your abilities for drawing, designing and spatial imagination. Simple Platonic solids consist of simple polygons, which are identical to each other in one figure. So, a tetrahedron is three isosceles triangles. Before building a sweep, you need to imagine how to properly fold flat polygons together to get a polyhedron. Triangles can be connected to each other along the edges by drawing one next to the other. To glue the development of polyhedrons, the schemes must be equipped with special pockets or valves that will allow you to connect all the parts into a single whole. A tetrahedron is the simplest figure with four faces. An octahedron can be represented as a double tetrahedron, it has eight garni - isosceles triangles. A hexahedron is a cube familiar to everyone since childhood. An icosahedron is a compound of 20 isosceles triangles into a regular convex polyhedron. A dodecahedron is a volumetric figure of 12 faces, each of which is a regular pentagon.
Subtleties of work
Building a net of a polyhedron and gluing a paper model out of it is a delicate matter. The scan, of course, can be taken already prepared. And you can, with some effort, build it yourself. But in order to make a full-fledged three-dimensional model of a polyhedron, you need to assemble it. A polyhedron is best made from thick paper, which holds its shape well and does not warp from glue. All lines thatmust be bent, it is best to pre-punch, using, for example, a non-writing ballpoint pen or the back of a knife blade. This nuance will help to fold the model more accurately, respecting the dimensions and directions of the edges.
If you make different polyhedrons from colored paper, then such models can be used as decorative elements that decorate the room - a children's room, an office, a living room. By the way, polyhedra can be called a unique find of decorators. Modern materials allow creating original interior items based on geometric shapes.
