An Octahedron is the three-dimensional cross polytope. It is the dual of a cube - in other words, it is a cube where all vertices have been replaced with faces and all faces have been replaced with vertices. It is also the triangular antiprism, a fact that can clearly be seen from its graph. In addition it is a square bipyramid, meaning it is composed of two square pyramids stuck together at their bases. The dihedral angle of an octahedron is the arcos(-13). The octahedron has four triangle meeting at a vertex.
Jonathan Bowers calls the octahedron an Oct, a shortened form of its name. The Higher Dimensions wiki sometimes calls this shape an Aerohedron, from aero- referring to a cross polytope and -hedron referring to three dimensions.
The octahedron is composed of 8 triangles, with four of them meeting at each vertex. It is formed of two suare pyramids joined together. It is also a triangular antiprism, composed of two triangles, in dual orientations, joined by a band of 6 triangles.
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