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Hexahedron
✖
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

open allclose all

Basic Examples  (3)Summary of the most common use cases

A hexahedron:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-f8gaof
Out[1]=1

A styled hexahedron:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-sxptmj
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-84fmk
Out[2]=2

Volume and centroid:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-zpy9vm
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-kgn009
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-hd55qh
Out[3]=3

Scope  (18)Survey of the scope of standard use cases

Graphics  (8)

Specification  (2)

A single hexahedron:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-ce4k03
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-ggb1ww
Out[2]=2

Multiple hexahedrons:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-1c6641
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-h7cw3f
In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-ppozsb
Out[3]=3

Styling  (3)

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

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-38df6s
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-78t7nc
Out[2]=2

Apply a Texture to the faces:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-vff8kd
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-5tt6t
Out[2]=2

Assign VertexColors to vertices:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-2h0wgx
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-twbbe6
Out[2]=2

Coordinates  (3)

Specify coordinates by fractions of the plot range:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-prz04t
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-u8d4ip
Out[2]=2

Specify scaled offsets from the ordinary coordinates:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-po136z
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-6qq3xm
Out[2]=2

Points can be Dynamic:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-3sh852
Out[1]=1

Regions  (10)

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

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-e3gvsm
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-y220
Out[2]=2

Geometric dimension is the dimension of the shape itself:

In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-bx9tom
Out[3]=3

Membership testing:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-j5s1r5
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-p89qc
Out[2]=2

Get conditions for point membership:

In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-d9nxgd
Out[3]=3

Volume:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-se0twe
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-e06l44
Out[2]=2

Centroid:

In[3]:=3
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https://wolfram.com/xid/0tqnzefqf8y3zm-gwq4b4
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-oknxhk
Out[4]=4

Distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-i8cqms
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-bruj1e
Out[2]=2

The equidistance contours for a hexahedron:

In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-jdsxbg
Out[3]=3

Signed distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-h7eno
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-b7y6q0
Out[2]=2

Nearest point in the region:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-6fqw5x
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-et4yza
Out[2]=2

Nearest points to an enclosing sphere:

In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-e29k5d
In[4]:=4
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-5ksoo8
In[5]:=5
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-g70sch
Out[5]=5

A hexahedron is bounded:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-yw9mlv
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-wv3700
Out[2]=2

Find its range:

In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-p10u0d
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-h2d2dj
Out[4]=4

Integrate over a hexahedron region:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-c81tiw
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-banwkr
Out[2]=2

Optimize over a hexahedron region:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-fdvdlz
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-hyz4dq
Out[2]=2

Solve equations in a hexahedron region:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-hzsonx
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-cn6ygq
Out[2]=2

Applications  (4)Sample problems that can be solved with this function

Convert a Cuboid to a Hexahedron:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-4oja0n
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-0walhg
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-k2amp6
Out[3]=3

Convert a Parallelepiped to a Hexahedron:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-yhh4gh
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-swkgj9
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-lexi2a
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-fezsch
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-mc91r4
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-qxe5bt
Out[3]=3

Create a tiling of hexahedra:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-1ykska
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-o8u6ym
Out[2]=2

Properties & Relations  (4)Properties of the function, and connections to other functions

Hexahedron is a generalization of a Cuboid in dimension 3:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-c1q2ki
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-0uif6
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-u32usv
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-h426c
Out[2]=2

Point index list of tetrahedra vertices:

In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-mtv2bj
In[4]:=4
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-sos1yg
Out[4]=4

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

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-jufwh0
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-ehckv7
In[3]:=3
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-cc9t05
Out[3]=3

ImplicitRegion can represent any Hexahedron:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-hw5ae3
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-jmnohi
Out[2]=2

Neat Examples  (2)Surprising or curious use cases

Random collection of hexahedrons:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-fbt4h6
Out[1]=1

Sweep a hexahedron around an axis:

In[1]:=1
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-n4ssvr
In[2]:=2
✖
https://wolfram.com/xid/0tqnzefqf8y3zm-fpl7yf
Out[2]=2
Wolfram Research (2014), Hexahedron, Wolfram Language function, https://reference.wolfram.com/language/ref/Hexahedron.html (updated 2019).
✖
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).

✖
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.

✖
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

✖
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: 02-May-2025 ]}

✖
@misc{reference.wolfram_2025_hexahedron, author="Wolfram Research", title="{Hexahedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Hexahedron.html}", note=[Accessed: 02-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: 02-May-2025 ]}

✖
@online{reference.wolfram_2025_hexahedron, organization={Wolfram Research}, title={Hexahedron}, year={2019}, url={https://reference.wolfram.com/language/ref/Hexahedron.html}, note=[Accessed: 02-May-2025 ]}