oktahédral

Oktahédral is a term used to describe objects with eight faces, and in many contexts it corresponds to what English speakers call octahedral. The word is formed from Greek roots meaning eight and face. In everyday geometry, oktahédral often refers to the eight-faced polyhedra as a class, with the regular octahedron being the most familiar example.

The regular octahedron, the prototypical oktahédral solid, has eight equilateral triangular faces, six vertices, and twelve edges. It is one of the five Platonic solids and is dual to the cube. The symmetry of a regular oktahédral solid is high, described by the full symmetry group Oh. For an edge length a, its volume is (√2/3) a^3, the circumscribed radius is a√2/2, and the inradius is a√6/6.

In practice, the term oktahédral also appears in related areas. In chemistry and crystallography, octahedral geometry describes a central atom surrounded by six ligands located at the vertices of an octahedron. In materials science and tiling, variations such as the truncated octahedron illustrate space-filling behavior. In popular culture and gaming, eight-sided dice used in tabletop RPGs are commonly based on octahedral shapes.

Overall, oktahédral denotes eight-faced geometry, with the regular octahedron as its most prominent representative, notable for its symmetry, dual relationship to the cube, and diverse appearances in science, mathematics, and gaming.