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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.

Other Names

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.

It can also be called a rectified tetrahedron or tetratetrahedron, as it can be made by truncating a tetrahedron to the midpoints of the edges. In this form it can be represented as .


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.



For more information on the shape:

[1]Go clicc the lincc

See also

Zeroth First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth
Simplex Point Line Triangle Tetrahedron Pentachoron Hexateron Heptapeton Octaexon Enneazetton Decayotton Hendecaxennon
Hypercube Point Line Square Cube Tesseract Penteract Hexeract Hepteract Octeract Enneract Dekeract
Cross Point Line Square Octahedron Hexadecachoron Pentarss Hexarss Heptarss Octarss Ennearss Decarss
Hypersphere Point Line Circle Sphere Glome Hyperglome Hexaphere Heptaphere Octaphere Enneaphere Decaphere