Octahedron – one of four regular polyhedrons to which people attached magic significance in antique times. This polyhedron symbolized air. The demonstration model of an octahedron can be made of dense paper or a wire.

## It is required to you

- - dense paper or cardboard;
- - ruler;
- - pencil;
- - protractor;
- - scissors;
- - PVA glue.

## Instruction

1. At an octahedron eight sides, each of which represents an equilateral triangle. In geometry usually build the octahedron entered in a cube or described about it. To make model of this solid, difficult calculations will not be necessary. The octahedron will consist of two identical tetrahedral pyramids which are stuck together among themselves.

2. On the sheet of paper draw a square. On one of its parties construct the correct triangle at which all parties are equal, and each of corners makes 60 °. It is convenient to build a triangle by means of a protractor, having postponed from two corners of a square, adjacent to the same party, on 60 °. Through marks carry out beams. The point from crossing will also be the third corner, and further – pyramid top. Construct the same triangles on other parties of a square.

3. You should stick together a pyramid. For this purpose allowances will be necessary. There are enough four allowances, on one on each triangle. Cut out what at you turned out. Make the second same preparation. Bend lines of a bend on inner side.

4. Bend each of triangles on inner side. Smear allowances with PVA glue. Stick together two identical pyramids and let's them dry.

5. Now it is necessary to stick together pyramids together. Smear a square bottom of one of them with glue, press a bottom of the second, having combined the parties and corners. Let's an octahedron dry out.

6. To make octahedron model of a wire, you need a cardboard or wooden square. However, it is possible to manage also a usual triangle – to bend preparation at right angle, it quite enough. Bend a square from a wire.

7. Cut off 4 identical pieces of a wire of 2 parties in size of a square, plus an allowance for fastening them in two points among themselves, and if necessary – to attach also to square corners. It depends on a wire. If material can be soldered, length of sides is equal to the doubled party of a square without any allowances.

8. Find the middle of a piece, a primotayta or solder it to a square corner. In the same way attach other preparations. Connect the ends of edges which are on one side of the square basis among themselves. The correct triangles will turn out by itself. Do the same operation also with the ends of edges which are on other side of the basis. The octahedron is ready.