Difference between revisions of "Octahedron"
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==Definition== | ==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 | + | 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 four meeting at each [[vertex]]. |
| − | The [[regular | + | The [[regular Octahedron|regular octahedron]] has eight [[equilateral triangle]] faces and is one of the five [[Platonic solid]]s. It has six vertices, twelve edges, and is [[Platonic solid #Duality | dual]] to the [[cube (geometry)|cube]]. |
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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. | ||
Latest revision as of 17:48, 5 September 2024
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 four 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
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 
