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 .
Structure
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.
Hypervolumes
Subfacets
- 6 points (0D)
- 12 lines segments (1D)
- 8 triangles (2D)
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 |