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Cuboid
✖
Cuboid

✖
Cuboid[pmin]

represents a unit hypercube with its lower corner at pmin.

✖
Cuboid[pmin,pmax]

represents an axis-aligned filled cuboid with lower corner pmin and upper corner pmax.

Details and Options

Examples

open allclose all

Basic Examples  (5)Summary of the most common use cases

A unit cuboid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-poi6w
Out[1]=1

Two unit cuboids:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-xi5uq
Out[1]=1

Cuboids with different sizes:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-kpxblr
Out[1]=1

Differently styled cuboids:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-84fmk
Out[1]=1

Volume and centroid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-jnnwyy
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-errv1m
Out[2]=2

Scope  (21)Survey of the scope of standard use cases

Graphics  (11)

Specification  (3)

A unit cube:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-jeocjz
Out[2]=2

A unit square:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-v9245o
Out[2]=2

A cuboid parallel to each axis:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-g4ux8r
Out[1]=1

Short form for a unit cube cornered at the origin:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-gsjlwb
Out[1]=1

Styling  (5)

Color directives specify the face colors of cuboids:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-bi6d9l
Out[1]=1

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

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-cjf4xd
Out[1]=1

Different properties can be specified for the front and back of faces using FaceForm:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-sa7ne
Out[1]=1

Cuboid with different specular exponents:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-d1tyd0
Out[1]=1

White cuboid that glows red:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-ca9zt
Out[2]=2

Opacity specifies the face opacity:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-v6995
Out[1]=1

Coordinates  (3)

Use Scaled coordinates:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-zlfm8
Out[1]=1

Specify scaled offsets from the ordinary coordinates:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-nn6a0g
Out[1]=1

Points can be Dynamic:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-6gl1zz
Out[1]=1

Regions  (10)

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

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-y220
Out[1]=1

Geometric dimension is the dimension of the shape itself:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-bx9tom
Out[2]=2

Membership testing:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-c7lq97
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-f70gib
Out[2]=2

Get conditions for point membership:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-2p4iz
Out[3]=3

Volume:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-se0twe
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-e06l44
Out[2]=2

Centroid:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-gwq4b4
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0bdo648n1-oknxhk
Out[4]=4

Distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-oc6hy
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-bruj1e
Out[2]=2

The equidistance contours for a cuboid:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-lk4lze
Out[3]=3

Signed distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-cybvpc
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-b7y6q0
Out[2]=2

Nearest point in the region:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-d7g53y
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-mtue
Out[2]=2

Nearest points to an enclosing sphere:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-e29k5d
In[4]:=4
✖
https://wolfram.com/xid/0bdo648n1-5ksoo8
In[5]:=5
✖
https://wolfram.com/xid/0bdo648n1-uv1cfm
Out[5]=5

A cuboid is bounded:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-hycz8p
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-dym4fu
In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-i3tfrr
Out[3]=3

Find its range:

In[4]:=4
✖
https://wolfram.com/xid/0bdo648n1-l3exhn
Out[4]=4

Integrate over a cuboid region:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-fivgav
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-banwkr
Out[2]=2

Optimize over a cuboid region:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-nf9ton
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-hyz4dq
Out[2]=2

Solve equations in a cuboid region:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-bximqe
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-cn6ygq
Out[2]=2

Applications  (8)Sample problems that can be solved with this function

Define a cuboid region by length, width, and height:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-cep5j8

Compute its volume:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-8j3mws
Out[2]=2

Visualize some instances:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-6yafj7
Out[3]=3

Total mass for a cuboid region with density given by :

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-h2ora
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-p48pf6
Out[2]=2

Find the mass of ethanol in a cuboid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-u48x65

Density of ethanol:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-6bgb0m
Out[2]=2

Volume of cuboid:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-6fqwu0
Out[3]=3

Mass of ethanol in the cuboid:

In[4]:=4
✖
https://wolfram.com/xid/0bdo648n1-8she50
Out[4]=4

Create a bounding box from RegionBounds:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-qi3v3e
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-xtn5yp

Compute the bounding box:

In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-e0g9la

Compute the difference in Volume:

In[4]:=4
✖
https://wolfram.com/xid/0bdo648n1-na8g4o
Out[4]=4

Visualize the bounding box:

In[5]:=5
✖
https://wolfram.com/xid/0bdo648n1-gf19ex
Out[5]=5

A simple 3D bar chart:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-hjiwd
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-89fpz
Out[2]=2

Show a sequence of steps in the evolution of a 3D cellular automaton:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-ohujb
Out[1]=1

Use as a simple way to visualize volumes:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-gyp148
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-h3vc45
Out[2]=2

Hyperboloids:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-j04i9t
Out[1]=1

Properties & Relations  (8)Properties of the function, and connections to other functions

Use Transpose to convert Cuboid to a range specification:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-85p26m
Out[1]=1

And conversely, a range specification to a Cuboid specification:

In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-c74hf9
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0bdo648n1-oi7uuo
Out[3]=3

Use Rotate to get all possible cuboids in Graphics3D:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-7nna6
Out[1]=1

Polygon is a generalization of Cuboid in 2D:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-qrw1uh
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-md2497
Out[2]=2

Rectangle is a special case of Cuboid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-nqjym6
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-zonlw2
Out[2]=2

Hexahedron is a generalization of Cuboid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-c1q2ki
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-zr79nf
Out[2]=2

ImplicitRegion can represent any Cuboid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-hw5ae3
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-pgs8le
Out[2]=2

Parallelepiped can represent any Cuboid:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-ibvi4f
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-0zx4zc
Out[2]=2

Cuboid is a norm ball for the -norm:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-mysp6a
In[2]:=2
✖
https://wolfram.com/xid/0bdo648n1-b56hh2
Out[2]=2

Neat Examples  (3)Surprising or curious use cases

Random cuboid collections:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-dgvoyq
Out[1]=1

Sweep a cuboid around an axis:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-wgo0zk
Out[1]=1

A pyramid with random color cubes:

In[1]:=1
✖
https://wolfram.com/xid/0bdo648n1-dksy6h
Out[1]=1
Wolfram Research (1991), Cuboid, Wolfram Language function, https://reference.wolfram.com/language/ref/Cuboid.html (updated 2019).
✖
Wolfram Research (1991), Cuboid, Wolfram Language function, https://reference.wolfram.com/language/ref/Cuboid.html (updated 2019).

Text

Wolfram Research (1991), Cuboid, Wolfram Language function, https://reference.wolfram.com/language/ref/Cuboid.html (updated 2019).

✖
Wolfram Research (1991), Cuboid, Wolfram Language function, https://reference.wolfram.com/language/ref/Cuboid.html (updated 2019).

CMS

Wolfram Language. 1991. "Cuboid." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Cuboid.html.

✖
Wolfram Language. 1991. "Cuboid." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Cuboid.html.

APA

Wolfram Language. (1991). Cuboid. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cuboid.html

✖
Wolfram Language. (1991). Cuboid. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cuboid.html

BibTeX

@misc{reference.wolfram_2025_cuboid, author="Wolfram Research", title="{Cuboid}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Cuboid.html}", note=[Accessed: 25-March-2025 ]}

✖
@misc{reference.wolfram_2025_cuboid, author="Wolfram Research", title="{Cuboid}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Cuboid.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_cuboid, organization={Wolfram Research}, title={Cuboid}, year={2019}, url={https://reference.wolfram.com/language/ref/Cuboid.html}, note=[Accessed: 25-March-2025 ]}

✖
@online{reference.wolfram_2025_cuboid, organization={Wolfram Research}, title={Cuboid}, year={2019}, url={https://reference.wolfram.com/language/ref/Cuboid.html}, note=[Accessed: 25-March-2025 ]}