tetraëdren

A tetraëder is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. It is one of the five Platonic solids, meaning all its faces are congruent regular polygons and the same number of faces meet at each vertex. In the case of a regular tetraëder, all four faces are equilateral triangles.

The tetraëder is the simplest of all the convex polyhedra. It can be thought of as a triangular pyramid where the base is also a triangle congruent to the other three faces. The symmetry group of a regular tetraëder is the tetrahedral group, which has 24 elements.

Tetraëdra are found in nature and in various fields of science and mathematics. For instance, the tetrahedron is a fundamental unit in crystallography. In chemistry, the methane molecule (CH4) has a tetrahedral structure, with the carbon atom at the center and the four hydrogen atoms at the vertices. This geometry is crucial for understanding molecular shapes and reactivity.

In mathematics, the tetraëder is a common object of study in geometry and topology. It is the three-dimensional simplex, a generalization of a triangle in two dimensions and a line segment in one dimension. The volume of a regular tetraëder with edge length 'a' can be calculated using the formula V = (a^3) / (6 * sqrt(2)). The surface area is given by A = sqrt(3) * a^2.