Develop spatial imagination

0.00 $
0 item(s)

Tetrahedron. How to make pdf template

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

The formula determines the radius of the described sphere of the tetrahedron:

Where "a" is the side length.

The sphere can be inscribed inside the tetrahedron.

The formula determines the radius of the inscribed sphere of a tetrahedron:

The surface area of a tetrahedron

The surface area of a tetrahedron can be represented as a shape net area.
The tetrahedron surface area can be defined as the area of one of the tetrahedron's sides. This is the area of a regular triangle, multiplied by 4. Or use the formula:

The following formula determines the volume of the tetrahedron:

The following formula determines the height of the tetrahedron:

The formula determines the distance to the center of the base of the tetrahedron:

Tetrahedron shape nets

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

Choose a color for your polyhedron.

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

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

Video. The rotation of all regular polyhedra

Tetrahedron. How to make pdf template

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".

Mathematical characteristics of a tetrahedron

Popular