Octahedron

The octahedron is one of the five Platonic solids. It consists of 8 equilateral triangles, joined 4 to a square vertex. It is the 3 dimensional orthoplex.

It can be built by joining two square pyramids by their square face, which makes it the square bipyramid. It is also the uniform triangular antiprism.

Vertex coordinates
An octahedron of side length 1 has vertex coordinates given by all permutations of (±$\sqrt{2}$/2, 0, 0).

Tetratetrahedron
The tetratetrahedron, or tatet, is a variant of the octahedron with A3 symmetry. It consists of two types of equilateral triangles. It can be constructed as a rectification of the tetrahedron. It can be represented as o3x3o.

Related polyhedra
The octahedron is the colonel of a two-member regiment that also includes the tetrahemihexahedron.

The octahedron is the regular-faced square bipyramid. If a cube, seen as a square prism, is inserted between the two haves, the result is an elongated square bipyramid.