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Tetrahedron

Tetrahedron

The ancient Greeks gave the polyhedron a name according to the number of faces. "Tetra" means four, "hedra" means the face (tetrahedron - a solid having four faces).

Therefore, the question "What is a tetrahedron?", We can give the following definition: "Tetrahedron is a geometric solid of four faces, each of which is a regular triangle."

Polyhedron refers to the regular polyhedra and is one of the five Platonic solids.

The tetrahedron has the following characteristics:

    The type of the face is the right triangle;
    
The number of sides at the face is 3;
    
The total number of faces is 4;
    
The number of edges adjacent to the vertex is 3;
    
The total number of vertices is 4;
    
The total number of edges is 6;

The regular tetrahedron is composed of four equilateral triangles. Each vertex of it is a vertex of three triangles. Therefore, the sum of flat angles at each vertex is 180 °.
The tetrahedron has no center of symmetry, but has 3 axes of symmetry and 6 planes of symmetry.

Is the tetrahedron a pyramid? Yes, the tetrahedron is a triangular pyramid whose all sides are equal.

Can a pyramid be a tetrahedron? Only if it is a pyramid with a triangular base and each of its sides is an equilateral triangle.

 

Mathematical characteristics of a tetrahedron

1 Tetrahedron opis

The tetrahedron can be placed in a sphere (inscribed), so that each of its vertices will touch the inner wall of the sphere.

The radius of the described sphere of the tetrahedron is determined by the formula

:

Tetrahedron R tetr

 , where "a" is the side length .

Сфера вписанная в тетраэдр

The sphere can be inscribed inside the tetrahedron.

The radius of the inscribed sphere of a tetrahedron is determined by the formula:

 

Tetrahedron r1 tetr

площадь поверхности тетраэдра

Surface area of a tetrahedron

The surface area of the tetrahedron can be represented in the form of the net area. The surface area can be defined as the area of one of the sides of the tetrahedron (this is the area of a regular triangle) multiplied by 4. Or use the formula: Tetrahedron S tetr

Объем тетраэдра

The volume of the tetrahedron is determined by the following formula:

V Tetrahedron

Tetrahedron nets

Tetrahedron can be made yourself. Paper or cardboard is the most suitable material. For the assembly will require paper net - a single part with the lines of the folds.

plato 1 lg
Choosing a color for a polyhedron.

The ancient Greek philosopher Plato associated the tetrahedron with the "earth" element - fire, therefore, to build a model of this regular polyhedron, we chose red.

Tetrahedron ris2

The figure shows the net of a tetrahedron:

Note that this is not the only net option.

To build a model, you can download a net in pdf format and print it on an A4 sheet:
- if you print on a color printer - color net.
- if you will use for the assembly of colored cardboard - net.

Video. Tetrahedron from the set "Magic Edges"

You can make a model of a tetrahedron using the parts for assembling from the set "Magic Edges".

12 obl 400

Video. Build a polyhedron from a set:

Video. Rotation of the finished polyhedron:

Video. Rotation of all regular polyhedra

 

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