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 a surface area shape net. 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 shape 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. The build a polyhedron from the set:

 

Detailed assembly from Alexei Zhigulev (youtube channel - Origami)

 

Video. The rotation of the finished polyhedron:

Video. The rotation of all regular polyhedra

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