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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 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 where 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

The tetrahedron placed in a sphere

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

:

formula The radius of the described sphere

 , where "a" is the side length .

The sphere inscribed inside the tetrahedron

The sphere can be inscribed inside the tetrahedron.

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

 

formula The radius of the inscribed sphere of a tetrahedron

Surface area of a tetrahedron

Surface area of a tetrahedron

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: formula Surface area of a tetrahedron

The volume of the tetrahedron

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

formula The volume of the tetrahedron

Tetrahedron height

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

tetrahedron height formula

The distance to the center of the base of the tetrahedron is determined by the formula:

 distance to the center of the tetrahedron

Tetrahedron nets

You can make a tetrahedron by yourself. Paper or cardboard is the most suitable material. For assembly, you will need a paper net—a single sheet with lines for all the folds.

plato
Choose a color for your 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 net

The figure shows the net of a tetrahedron:

Note that this is not the only option for a tetrahedron net.

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 - standard net.

Video. Tetrahedron from the "Magic Edges" set

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

magic edges 12

Video. Build a polyhedron from the set:

Video. Rotation of the finished polyhedron:

Video. Rotation of all regular polyhedra

 

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