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Wolfram Language & System Documentation Center
Cuboid
  • See Also
    • Cube
    • Hexahedron
    • Parallelogram
    • Rectangle
    • Simplex
    • Polyhedron
    • CanonicalizePolyhedron
    • BoundingRegion

    • Formats
    • VTK
  • Related Guides
    • Graphics Objects
    • Basic Geometric Regions
    • Solid Geometry
    • Symbolic Graphics Language
    • Polyhedra
  • Tech Notes
    • Three-Dimensional Graphics Primitives
    • See Also
      • Cube
      • Hexahedron
      • Parallelogram
      • Rectangle
      • Simplex
      • Polyhedron
      • CanonicalizePolyhedron
      • BoundingRegion

      • Formats
      • VTK
    • Related Guides
      • Graphics Objects
      • Basic Geometric Regions
      • Solid Geometry
      • Symbolic Graphics Language
      • Polyhedra
    • Tech Notes
      • Three-Dimensional Graphics Primitives

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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Graphics  
Specification  
Styling  
Coordinates  
Regions  
Applications  
Properties & Relations  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • Cube
    • Hexahedron
    • Parallelogram
    • Rectangle
    • Simplex
    • Polyhedron
    • CanonicalizePolyhedron
    • BoundingRegion

    • Formats
    • VTK
  • Related Guides
    • Graphics Objects
    • Basic Geometric Regions
    • Solid Geometry
    • Symbolic Graphics Language
    • Polyhedra
  • Tech Notes
    • Three-Dimensional Graphics Primitives
    • See Also
      • Cube
      • Hexahedron
      • Parallelogram
      • Rectangle
      • Simplex
      • Polyhedron
      • CanonicalizePolyhedron
      • BoundingRegion

      • Formats
      • VTK
    • Related Guides
      • Graphics Objects
      • Basic Geometric Regions
      • Solid Geometry
      • Symbolic Graphics Language
      • Polyhedra
    • Tech Notes
      • Three-Dimensional Graphics Primitives

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

  • Cuboid is also known as interval, rectangle, square, cube, rectangular parallelepiped, tesseract, hypercube, orthotope, hyperrectangle, and box.
  • Cuboid represents the region where and .
  • Cuboid[] is equivalent to Cuboid[{0,0,0}].
  • CanonicalizePolyhedron can be used to convert a cuboid to an explicit Polyhedron object.
  • Cuboid can be used in Graphics and Graphics3D.
  • In graphics, the points pmin and pmax can be Scaled, ImageScaled, Offset, and Dynamic expressions.
  • Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.

Examples

open all close all

Basic Examples  (5)

A unit cuboid:

Two unit cuboids:

Cuboids with different sizes:

Differently styled cuboids:

Volume and centroid:

Scope  (21)

Graphics  (11)

Specification  (3)

A unit cube:

A unit square:

A cuboid parallel to each axis:

Short form for a unit cube cornered at the origin:

Styling  (5)

Color directives specify the face colors of cuboids:

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

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

Cuboid with different specular exponents:

White cuboid that glows red:

Opacity specifies the face opacity:

Coordinates  (3)

Use Scaled coordinates:

Specify scaled offsets from the ordinary coordinates:

Points can be Dynamic:

Regions  (10)

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

Signed distance from a point:

Nearest point in the region:

Nearest points to an enclosing sphere:

A cuboid is bounded:

Find its range:

Integrate over a cuboid region:

Optimize over a cuboid region:

Solve equations in a cuboid region:

Applications  (8)

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

Compute its volume:

Visualize some instances:

Total mass for a cuboid region with density given by :

Find the mass of ethanol in a cuboid:

Density of ethanol:

Volume of cuboid:

Mass of ethanol in the cuboid:

Create a bounding box from RegionBounds:

Compute the bounding box:

Compute the difference in Volume:

Visualize the bounding box:

A simple 3D bar chart:

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

Use as a simple way to visualize volumes:

Hyperboloids:

Properties & Relations  (8)

Use Transpose to convert Cuboid to a range specification:

And conversely, a range specification to a Cuboid specification:

Use Rotate to get all possible cuboids in Graphics3D:

Polygon is a generalization of Cuboid in 2D:

Rectangle is a special case of Cuboid:

Hexahedron is a generalization of Cuboid:

ImplicitRegion can represent any Cuboid:

Parallelepiped can represent any Cuboid:

Cuboid is a norm ball for the -norm:

Neat Examples  (3)

Random cuboid collections:

Sweep a cuboid around an axis:

A pyramid with random color cubes:

See Also

Cube  Hexahedron  Parallelogram  Rectangle  Simplex  Polyhedron  CanonicalizePolyhedron  BoundingRegion

Formats: VTK

Function Repository: RoundedCuboid

Tech Notes

    ▪
  • Three-Dimensional Graphics Primitives

Related Guides

    ▪
  • Graphics Objects
  • ▪
  • Basic Geometric Regions
  • ▪
  • Solid Geometry
  • ▪
  • Symbolic Graphics Language
  • ▪
  • Polyhedra

Related Links

  • An Elementary Introduction to the Wolfram Language : Coordinates and Graphics
  • NKS|Online  (A New Kind of Science)

History

Introduced in 1991 (2.0) | Updated in 2014 (10.0) ▪ 2019 (12.0)

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).

CMS

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

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: 01-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_cuboid, organization={Wolfram Research}, title={Cuboid}, year={2019}, url={https://reference.wolfram.com/language/ref/Cuboid.html}, note=[Accessed: 01-May-2026]}

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