RandomPolyhedron

RandomPolyhedron[spec]

gives a pseudorandom polyhedron with the specified specification spec.

RandomPolyhedron[spec,k]

gives a list of k pseudorandom polyhedra.

Details and Options

Examples

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Basic Examples  (2)

Generate a random convex hull polyhedron:

Generate a list of random polyhedra:

Compute the volume:

Scope  (4)

Basic Uses  (1)

Generate a random polyhedron with a specified property:

Convex Hull Polyhedra  (3)

Generate a random convex hull polyhedron:

Generate a list of random convex hull polyhedra:

Generate a random convex hull polyhedron from the Dirichlet distribution:

Uniform distribution:

Normal distribution:

Options  (2)

DataRange  (1)

DataRange allows you to specify the range of vertex points to generate:

Specify a different range:

WorkingPrecision  (1)

Generate a random polyhedron using machine arithmetic:

Using 30 digits of precision:

Applications  (3)

Basic Uses  (2)

Random polyhedra with 10 vertex points:

Generate random polyhedra for testing algorithms and verification of time complexity:

Time complexity for algorithms for convex polyhedra:

Geometry Probability  (1)

Simulate random convex polyhedra and compute volumes:

Estimate distribution:

Compare its histogram to the PDF:

Average volume of polyhedra with 10 vertices over a unit square:

Properties & Relations  (5)

Use SeedRandom to get repeatable random polyhedra:

Use BlockRandom to block one use of RandomPolyhedron from affecting others:

Use ConvexPolyhedronQ to check the property of a random polyhedron:

The OuterPolyhedron of a random polyhedron is simple:

Random polyhedra do not have voids:

Using PolyhedronDecomposition to decompose a polyhedron into tetrahedra:

Neat Examples  (1)

Random polyhedron collections:

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

Text

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

CMS

Wolfram Language. 2019. "RandomPolyhedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomPolyhedron.html.

APA

Wolfram Language. (2019). RandomPolyhedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomPolyhedron.html

BibTeX

@misc{reference.wolfram_2025_randompolyhedron, author="Wolfram Research", title="{RandomPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/RandomPolyhedron.html}", note=[Accessed: 05-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_randompolyhedron, organization={Wolfram Research}, title={RandomPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/RandomPolyhedron.html}, note=[Accessed: 05-May-2025 ]}