oktaedrid

An oktaedrid is a polyhedron with eight faces. The most common and well-known oktaedrid is the regular oktaedrid, which is one of the five Platonic solids. A regular oktaedrid has eight equilateral triangular faces, twelve edges, and six vertices. At each vertex, four faces meet. It can be thought of as two square pyramids joined at their bases.

The name "oktaedrid" comes from the Greek word "okto" meaning eight, and "hedra" meaning face. In crystallography, the oktaedrid is a common crystal form observed in minerals such as fluorite, diamond, and magnetite. The regular oktaedrid is dual to the cube; that is, if you place a vertex at the center of each face of a cube, the resulting polyhedron is a regular oktaedrid, and vice versa.

The surface area of a regular oktaedrid with edge length 'a' is given by the formula 2√3 * a^2. The volume of a regular oktaedrid with edge length 'a' is given by the formula (√2 / 3) * a^3. These properties make the oktaedrid a shape with significant geometric and mathematical interest, appearing in various fields of science and design.