Difference between revisions of "Octahedron"
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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]]. | 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]] 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]]. | ||
| + | [img]{http://paulscottinfo.ipage.com/polyhedra/platonic/octahedron/1octahedronL.gif}[/img] | ||
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. | 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. | ||
Revision as of 12:36, 16 August 2015
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. [img]{http://paulscottinfo.ipage.com/polyhedra/platonic/octahedron/1octahedronL.gif}[/img]
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
of a regular octahedron with side length 
is 
- The volume
of a regular octahedron with side length is 
of a regular octahedron with side length 
is 
of a regular octahedron with side length 
