Develop spatial imagination
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.
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 : , where "a" is the side length . The sphere can be inscribed inside the tetrahedron. The radius of the inscribed sphere of a tetrahedron is determined by the formula: 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: The volume of the tetrahedron is determined by the following formula: The height of the tetrahedron is determined by the following formula: The distance to the center of the base of the tetrahedron is determined by the formula:
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. 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. 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:
You can make a model of a tetrahedron using the parts for assembling from the "Magic Edges" set. Video. The build a polyhedron from the set: Detailed assembly from Alexei Zhigulev (youtube channel - Origami) Video. The rotation of the finished polyhedron:
Mathematical characteristics of a tetrahedron
Tetrahedron shape nets
- 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
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