Hexahedron

Hexahedron[{p1,p2,…,p8}]

represents a filled hexahedron with corners p1, p2, …, p8.

Hexahedron[{{p1,1,p1,2,…,p1,8},{p2,1,…},…}]

represents a collection of hexahedra.

Details and Options

Examples

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Basic Examples  (3)

A hexahedron:

A styled hexahedron:

Volume and centroid:

Scope  (18)

Graphics  (8)

Specification  (2)

A single hexahedron:

Multiple hexahedrons:

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:

Coordinates  (3)

Specify coordinates by fractions of the plot range:

Specify scaled offsets from the ordinary coordinates:

Points can be Dynamic:

Regions  (10)

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

Geometric dimension is the dimension of the shape itself:

Membership testing:

Get conditions for point membership:

Volume:

Centroid:

Distance from a point:

The equidistance contours for a hexahedron:

Signed distance from a point:

Nearest point in the region:

Nearest points to an enclosing sphere:

A hexahedron is bounded:

Find its range:

Integrate over a hexahedron region:

Optimize over a hexahedron region:

Solve equations in a hexahedron region:

Applications  (4)

Convert a Cuboid to a Hexahedron:

Convert a Parallelepiped to a Hexahedron:

Create a square frustum parameterized by base width, top width, and height:

Create a tiling of hexahedra:

Properties & Relations  (4)

Hexahedron is a generalization of a Cuboid in dimension 3:

A hexahedron can be represented as the union of five tetrahedra:

Point index list of tetrahedra vertices:

A hexahedron can also be represented as the union of six tetrahedra:

ImplicitRegion can represent any Hexahedron:

Neat Examples  (2)

Random collection of hexahedrons:

Sweep a hexahedron around an axis:

Wolfram Research (2014), Hexahedron, Wolfram Language function, https://reference.wolfram.com/language/ref/Hexahedron.html (updated 2019).

Text

Wolfram Research (2014), Hexahedron, Wolfram Language function, https://reference.wolfram.com/language/ref/Hexahedron.html (updated 2019).

CMS

Wolfram Language. 2014. "Hexahedron." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Hexahedron.html.

APA

Wolfram Language. (2014). Hexahedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Hexahedron.html

BibTeX

@misc{reference.wolfram_2025_hexahedron, author="Wolfram Research", title="{Hexahedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Hexahedron.html}", note=[Accessed: 30-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_hexahedron, organization={Wolfram Research}, title={Hexahedron}, year={2019}, url={https://reference.wolfram.com/language/ref/Hexahedron.html}, note=[Accessed: 30-May-2025 ]}