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

A lot of interesting things you can find for yourself in thosespheres 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 fascinating if they are encountered more closely. So the geometric 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 handsunusual, stylish things - this is fascinating creativity. Mastering different polyhedra on your own 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. Start working in this technology will helpsweep of the polyhedron.

## Different faces - different shapes

Polyhedra are a special sphere of geometry. They are simple - for example, the cubes that children play from an early age - and they are very, very complex. BuildingThe scanning of polyhedra for gluing is considered to berather complex area of construction andcreativity: you need not only to know the basics of drawing, the geometric features of space, but also to have spatial imagination that allows you to evaluate the correctness of the solution even at the design stage. But one can not do without one's imagination. To makesweep polygons out of paper, it is not enough to just 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 the initial classes I encountered at work lessons with work, the result of which was to become a paper cube. Most often the teacher gave out workpieces -of a cube polyhedron on thick paper withSpecial pockets designed for gluing together the model's faces into a single whole. This kind of work the pupils of the primary 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 usbecome interesting not on the school bench, but only when you can find in them something fascinating, capable of giving something new, unusual in the usual 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 hollows. Stellate polyhedra consist of these basic figures in different configurations. That's whythe sweep of the simple polyhedron makes it possible to draw, or rather nacherit, and then glue a star-shaped polyhedron from the paper.

## Correct and irregular stellate polyhedra

Folding the platonic bodies together inin a certain order, you can build a lot of star-shaped polyhedra - beautiful, complex, multi-component. But they will be called "irregular stellate polyhedra". There are only four regular 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. So, 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 you can put them togetherstar polyhedron. The development of the smallest star dodecaera 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, includingstar 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, for example, the most versatile of the Platonic convex polyhedra is the dodecahedron. In this geometric figure there are 12 absolutely identical faces, 30 edges and 12 vertices. To makeScanning the correct polyhedra for gluing, you need to apply a maximum of accuracy and care. 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 a polyhedron - at leaststar, even Platonic, it is even more interesting to build a sweep of the future model on its own, assessing 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. For gluingThe sweeps of the polyhedra of the circuit must beare equipped with special pockets or valves, which will allow to connect all parts in 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.

## Subtlety of work

Construct the development of a polyhedron and glue it togetherpaper model - 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 in order to make a full-scale volumetric model of a polyhedron, it is necessary to assemble it. Polyhedron is best made of thick paper, which holds 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 neater, with the dimensions 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 nursery, a study, a living room.By the way, polyhedra can be called a unique find of decorators. Modern materials allow creating original interior objects on the basis of geometric figures.