oktaedrinen

Oktaedrinen is a term appearing in several languages to denote octahedra, a class of polyhedra in geometry. In English, the plural is octahedra and the singular is octahedron. The regular octahedron is a Platonic solid comprised of eight equilateral triangle faces, six vertices, and twelve edges. Each vertex is the meeting point of four faces. It is the dual polyhedron of the cube, meaning that the vertices of the octahedron correspond to the faces of the cube and vice versa. Its Schläfli symbol is {3,4} and it has octahedral symmetry, the same as the symmetry of many crystal forms.

In chemistry and crystallography, the term octahedral (oktaedrinen) is used to describe a common coordination geometry around a central atom, typically with six ligands located at the vertices of an octahedron. Variants include distorted octahedra, where bond lengths and angles deviate from idealized values due to ligand effects or electronic factors.

Octahedra occur in minerals and natural crystals as well as in manufactured materials and dice. In mineralogy, octahedral crystals or crystal faces reflect the underlying symmetry and growth conditions. In mathematics and computer graphics, octahedra are used in mesh generation and geometric modeling due to their compatibility with cubes.

See also: cube, Platonic solids, coordination geometry, crystallography.