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An '''octahedron''' is a type of [[polyhedron]].

==Definition==
In Euclidean [[geometry]], an octahedron is any polyhedron with eight [[face]]s.  The term is most frequently to refer to a polyhedron with eight [[triangular]] faces, with three meeting at each [[vertex]]. 
The [[regular]] [[octahedron]] has eight [[equilateral triangle]] faces and is one of the five [[Platonic solid]]s.  It has six vertices, twelve edges, and is [[dual]] to the [[cube (geometry)|cube]].

The regular octahedron can be decomposed into two [[square (geometry)|square]] [[pyramid]]s by a plane constructed [[perpendicular]] to the space [[diagonal]] joining two opposite vertices.

==Related Formulae==
* The surface area <math>A</math> of a regular octahedron with side length <math>a</math> is <math>2\sqrt{3}a^2</math>
* The volume <math>V</math> of a regular octahedron with side length <math>a</math> is <math>\frac{1}{3} \sqrt{2}a^3</math>

==See also==
* [[Polyhedron]]

[[Category:Definition]]
[[Category:Geometry]]
[[Category:Platonic solids]]