oktahedra

An octahedron is a polyhedron with eight faces. The most common and regular form is the regular octahedron, which is one of the five Platonic solids. A regular octahedron 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 regular octahedron is the dual of the cube, meaning that if you place a vertex at the center of each face of a cube and connect the centers of adjacent faces, you form an octahedron. Conversely, the dual of an octahedron is a cube. Its symmetry group is the octahedral group, which is the same as the group of rotations of a cube.

Octahedra have various applications. In crystallography, mineral crystals often exhibit octahedral shapes. In geometry, they are used in tessellations and as building blocks for more complex polyhedra. In computer graphics, the octahedron is a fundamental shape for representing spatial data and rendering. The term "oktahedra" is a less common but sometimes used alternative spelling for octahedra.