Octahedron

This article is a stub. Help us out by expanding it. An octahedron is a type of polyhedron.

Definition

In Euclidean geometry, an octahedron is any polyhedron with eight faces. 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 solids. It has six vertices, twelve edges, and is dual to the cube.


The regular octahedron can be decomposed into two square pyramids by a plane constructed perpendicular to the space diagonal joining two opposite vertices.

Related Formulae

  • The surface area $A$ of a regular octahedron with side length $a$ is $2\sqrt{3}a^2$
  • The volume $V$ of a regular octahedron with side length $a$ is $\frac{1}{3} \sqrt{2}a^3$

See also

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