oktaedere

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

The dual of a cube is a regular oktaeder. This means that if you place a vertex at the center of each face of a cube and connect these vertices, you will form an oktaeder. Conversely, the dual of an oktaeder is a cube. The oktaeder has a high degree of symmetry. It possesses rotational symmetry of order 4 about axes passing through opposite vertices, rotational symmetry of order 3 about axes passing through the centers of opposite faces, and rotational symmetry of order 2 about axes passing through the midpoints of opposite edges.

In crystallography, the oktaeder is a common crystal form. Minerals such as fluorite and magnetite can crystallize in oktahedral shapes. In chemistry, the oktaedral geometry describes the arrangement of six atoms or ligands around a central atom, with the ligands positioned at the vertices of an oktaeder. This is a common coordination geometry for transition metal complexes. The word "oktaeder" originates from the Greek words "okto" meaning eight and "hedra" meaning seat or face.