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
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- 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
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Examples
open allclose allScope (18)
Graphics (8)
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:
Get conditions for point membership:
The equidistance contours for a hexahedron:
Nearest points to an enclosing sphere:
Integrate over 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:
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:
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