# Octahedron

represents a regular octahedron centered at the origin with unit edge length.

Octahedron[l]

represents an octahedron with edge length l.

Octahedron[{θ,ϕ},]

represents an octahedron rotated by an angle θ with respect to the z axis and angle ϕ with respect to the y axis.

Octahedron[{x,y,z},]

represents an octahedron centered at {x,y,z}.

# Details and Options

• Octahedron is also known as regular octahedron.
• Octahedron can be used as a geometric region and graphics primitive.
• is equivalent to Octahedron[{0,0,0},1].
• Octahedron[l] is equivalent to Octahedron[{0,0,0},l].
• CanonicalizePolyhedron can be used to convert a octahedron to an explicit Polyhedron object.
• Octahedron can be used in Graphics3D.
• In graphics, the points and edge lengths can be Scaled and Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, Texture and color.
• The following options and settings can be used in graphics:
•  VertexColors Automatic vertex colors to be interpolated VertexNormals Automatic effective vertex normals for shading VertexTextureCoordinates None coordinates for textures

# Examples

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## Basic Examples(3)

An octahedron:

A styled octahedron:

Volume and centroid:

## Scope(6)

### Graphics(4)

#### Specification(1)

A single octahedron:

#### Styling(3)

FaceForm and EdgeForm can be used to specify the styles of the faces and edges:

Apply a Texture to the faces:

Assign VertexColors to vertices:

### Regions(2)

Embedding dimension is the dimension of the space in which the octahedron lives:

Geometric dimension is the dimension of the shape itself:

An octahedron is bounded:

Find its range:

Wolfram Research (2019), Octahedron, Wolfram Language function, https://reference.wolfram.com/language/ref/Octahedron.html.

#### Text

Wolfram Research (2019), Octahedron, Wolfram Language function, https://reference.wolfram.com/language/ref/Octahedron.html.

#### CMS

Wolfram Language. 2019. "Octahedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Octahedron.html.

#### APA

Wolfram Language. (2019). Octahedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Octahedron.html

#### BibTeX

@misc{reference.wolfram_2022_octahedron, author="Wolfram Research", title="{Octahedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Octahedron.html}", note=[Accessed: 04-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_octahedron, organization={Wolfram Research}, title={Octahedron}, year={2019}, url={https://reference.wolfram.com/language/ref/Octahedron.html}, note=[Accessed: 04-June-2023 ]}