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

• Hexahedron can be used as a geometric region and a graphics primitive.
• Hexahedron represents a filled polyhedron given by the polygon faces {p4,p3,p2,p1}, {p1,p2,p6,p5}, {p2,p3,p7,p6}, {p3,p4,p8,p7}, {p4,p1,p5,p8}, and {p5,p6,p7,p8}.
• CanonicalizePolyhedron can be used to convert a hexahedron to an explicit Polyhedron object.
• Hexahedron can be used in Graphics3D.
• In graphics, the points pi 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

open allclose all

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_2024_hexahedron, author="Wolfram Research", title="{Hexahedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Hexahedron.html}", note=[Accessed: 25-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_hexahedron, organization={Wolfram Research}, title={Hexahedron}, year={2019}, url={https://reference.wolfram.com/language/ref/Hexahedron.html}, note=[Accessed: 25-July-2024 ]}