Octahedron

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Regular octahedron
Octahedron.svg
(Click here for rotatin model)
Type Platonic solid
Elements F = 8, E = 12
V = 6 (χ = 2)
Faces by sides 8{3}
Conway notation {{{O-conway}}}
Schläfli seembols {3,4}
r{3,3}
Face confeeguration {{{O-ffig}}}
Wythoff seembol 4 | 2 3
Coxeter diagram CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
Symmetry Oh, BC3, [4,3], (*432)
Rotation group O, [4,3]+, (432)
References U05, C17, W2
Properties regular, convexdeltahedron
Dihedral angle 109.47122° = arccos(-1/3)
Octahedron vertfig.png
3.3.3.3
(Vertex feegur)
Hexahedron.png
Cube
(dual polyhedron)
Octahedron flat.svg
Net

In geometry, an octahedron (plural: octahedra) is a polyhedron wi aicht faces. A regular octahedron is a Platonic solid componed o aicht equilateral triangles, fower o which meet at each vertex.

A regular octahedron is the dual polyhedron o a cube. It is a rectified tetrahedron. It is a square bipyramid in ony o three orthogonal orientations. It is an aa a triangular antiprism in ony o fower orientations.

An octahedron is the three-dimensional case o the mair general concept o a cross polytope.