The development of a polyhedron for gluing. Scanning a star polyhedron

A lot of interesting things can be found for oneself in those spheres of science, which, it would seem, will never be useful in the ordinary life of ordinary people. For example, geometry, which most people forget, just crossed the threshold of the school. But strangely, the unfamiliar areas of science become very exciting, if you come across them more closely. So the geometrical unfolding of the polyhedron - a completely unnecessary thing in everyday life - can become the beginning of fascinating creativity, capable of capturing both children and adults.

Beautiful geometry

Decorate the interior of the house, creating their own hands unusual, stylish things - this is fascinating creativity. Mastering different polyhedra yourself from thick paper means creating unique things that can become a simple occupation for a day or two, and 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 who, with the help of building sweeps according to the laws of geometry, make mock-ups of animals and various objects from paper. But this is a rather complex mathematical and drawing work. развертка многогранника. Start working in this technique will help sweep the polyhedron.

Different faces - different shapes

Polyhedra are a special sphere of geometry. They are simple - for example, cubes, which children play from an early age - but are very, very complex. достаточно сложной областью конструирования и творчества: нужно не только знать основы черчения, геометрические особенности пространства, но и иметь пространственное воображение, позволяющее оценить правильность решения еще на стадии проектирования. The construction of a sweep of polyhedra for gluing is considered a rather complex area of construction and creativity: one needs not only to know the basics of drawing, the geometric features of space, but also to have spatial imagination that allows to evaluate the correctness of the solution even at the design stage. But one can not do without one's imagination. To make sweeps of polygons from paper, it is not enough to simply imagine how the work should look like in the end. You need to be able to correctly calculate, design, and draw it correctly.

The very first polyhedron - a cube

Most likely, every person who attended school, even in primary classes, encountered work lessons with work, the result of which was to become a paper cube. развертки многогранника куба на плотной бумаге со специальными кармашками, предназначенными для склеивания граней модели в единое целое. Most often the teacher handed out workpieces - sweeps of the cube polyhedron on thick paper with special pockets intended for gluing the model's faces into a single whole. This kind of work the pupils of the elementary school could be proud of, because with paper, scissors, glue and their efforts, an interesting piece of art - a three-dimensional cube - was obtained.

Interesting faces

Surprisingly, many knowledge about the world around you is not interesting on the school bench, but only when you can find in them something fascinating, capable of giving something new, unusual in the ordinary 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 bodies - convex polyhedra consisting only of regular polygons. There are only five such bodies: a tetrahedron, an octahedron, a hexahedron (cube), an icosahedron, a dodecahedron. They are convex figures without depressions. Stellate polyhedra consist of these basic figures in various configurations. развертка многогранника простого позволяет нарисовать, вернее начерить, а затем и склеить из бумаги звездчатый многогранник. Therefore, the unfolding of a simple polyhedron allows you to draw, or rather to nurse, and then glue a star-shaped polyhedron from paper.

Correct and irregular stellate polyhedra

Folding the platonic bodies together in a certain order, you can build a lot of star-shaped multihair - beautiful, complex, multi-component. But they will be called "irregular stellate polyhedra". There are only four star polyhedra: a small star dodecahedron, a large star dodecahedron, a large dodecahedron and a large icosahedron. The unfolding of polyhedra for gluing will not be simple drawings. They, like the figures, will consist of several components. Thus, for example, a small star dodecahedron is constructed from 12 pentagonal equilateral pyramids, folded in the form of a regular dodecahedron. That is, for the beginning it is necessary to draw and glue 12 identical pieces of regular pyramids, consisting of 5 equal faces. And only then can a star-shaped polyhedron be made of them . The development of the smallest star dodecaere is a difficult and practically impossible task. To build it, you need to be able to fit on one plane connected to each other 13 sweeps of different geometric bodies.

Beauty in simplicity

All three-dimensional bodies constructed according to the laws of geometry will look fascinating, including a star-shaped polyhedron. The deployment of each element of any similar body must be performed as accurately as possible. And even the simplest three-dimensional polyhedrons, starting with the Platonic tetrahedron, are an amazing beauty of the harmony of the universe and human labor embodied in the paper model. Here, say, the most versatile of the Platonic convex polyhedra is the dodecahedron. развертки правильных многогранников для склеивания, нужно приложить максимум аккуратности и внимательности. In this geometric figure there are 12 absolutely identical faces, 30 edges and 12 vertices. To make the sweeps of the correct polyhedra for gluing, you need to apply the maximum of care and accuracy. And the larger the figure in size, the more accurate all measurements should be.

How to build a scan yourself?

Perhaps, in addition to gluing together a polyhedron - even a star, even a Platonic one - it is even more interesting to build a future model of the future model by own strength, evaluating its ability to draw, construct and spatial vobozheniye. Simple Platonic bodies consist of simple polygons that are identical in one figure. Thus, a tetrahedron is three isosceles triangles. Before you build a sweep, you need to imagine how to properly fold flat polygons together to get a polyhedron. Triangles can be connected among themselves along the edges, drawing one next to the other. To glue the sweep of polyhedrons, the circuits must be equipped with special pockets or valves, which will allow all parts to be combined into a single whole. Tetrahedron - the simplest figure of four faces. The octahedron can be represented as a double tetrahedron, it has eight garlands - isosceles triangles. Hexahedron is called a cube familiar to everyone since childhood. The icosahedron is a junction of 20 isosceles triangles into a regular convex polyhedron. The dodecahedron is a three-dimensional shape of 12 faces, each of which is a regular pentagon.

Subtleties of work

To build the development of a polyhedron and glue a paper model out of it is a delicate matter. The sweep, of course, can be taken already ready. And it is possible, having put the effort, to build it yourself. But to make a full-scale volumetric model of a polyhedron, it is necessary to assemble it. Polyhedron is best made of thick paper, which keeps the shape well and does not warp from the glue. All the lines that need to be bent are best pre-punched using, for example, a non-writing ballpoint pen or the back side of the knife blade. This nuance will help to fold the model more accurately, with the observance of the sizes and directions of the ribs.

If you make different polyhedrons of colored paper, then these models can be used as decorative elements decorating the room - a children's room, study, living room. By the way, polyhedra can be called a unique find of decorators. Modern materials allow to create original interior objects on the basis of geometric figures.