1, all four faces are triangles: the plane formed by any three sides is not the plane formed by the fourth side. The three faces formed by the four vertices are not mutually * * * faces. The lines connecting the four vertices are not on the planes of the other three vertices. The center of gravity, outer center, inner center and vertical center of tetrahedron all exist.

2. regular tetrahedron expansion: to expand it into a combination of an equilateral triangle and three isosceles triangles, you can first simplify the regular tetrahedron into a cube. Connect the vertices of the cube with the midpoints of the opposite sides to form an isosceles triangle. Connect the other three vertices of the cube with the midpoint of the opposite side to form another three isosceles triangles.

3. Tetrahedral cone expansion: usually refers to the tetrahedron expanding along a certain edge or a certain surface. Specifically, the expanded diagram of a regular pyramid consists of four isosceles triangles and a square. This kind of development diagram is widely used in origami, DIY and other fields.

The shape of tetrahedron and its application field

1, all four faces of a tetrahedron are triangles, and each face has three vertices and three sides. A tetrahedron has four vertices and six sides, and each vertex is connected with the other three vertices. This structure makes tetrahedron have strong stability and robustness.

2. Tetrahedron is widely used in the crystal structure analysis of physics. Crystal is a periodically arranged structure composed of atoms or molecules, and tetrahedron can be used to describe the arrangement of atoms or molecules in crystal. By analyzing the structure of tetrahedron, we can study the properties and behaviors of crystals, such as thermal conductivity and electrical conductivity.

3. Tetrahedrons are also widely used in molecular structure analysis in chemistry. Molecules are structures composed of atoms, and tetrahedrons can be used to describe the arrangement of atoms in molecules. By analyzing the structure of tetrahedron, we can study the properties and behaviors of molecules, such as chemical reactions and optical properties.

4. Tetrahedron is also applied to topology and geometry in mathematics. Topology is a branch of mathematics that studies the shape and deformation of space, and tetrahedron can be used to describe the shape and deformation of space. Geometry is a branch of mathematics that studies geometric properties such as shape, size, position and direction. Tetrahedron can be used to study the changes and relationships of geometric properties.