# OuterPolyhedron

OuterPolyhedron[poly]

gives the outer polyhedron of the polyhedron poly.

# Details

• OuterPolyhedron is also known as polyhedron outer shell.
• Typically used to decompose a polyhedron as a difference of simple polyhedra, even when the original construction of the polyhedron was using crossing curves etc.
• OuterPolyhedron is defined by the canonicalization performed in CanonicalizePolyhedron.
• OuterPolyhedron gives a polyhedron of the form Polyhedron[{p1,p2,},{{f1,f2,},}], where pk are explicit coordinates, and fk are integer lists referring to polygon faces.
• In general, the result will be a Polyhedron object representing a disjoint union of simple polygons.

# Examples

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## Basic Examples(1)

Get the outer polyhedron:

## Scope(3)

OuterPolyhedron works on polyhedrons:

Cube:

Polyhedron with holes:

Polyhedrons with disconnected components:

## Properties & Relations(2)

OuterPolyhedron of a simple polyhedron is the polyhedron itself:

A simple polyhedron has the same polyhedron coordinates as its OuterPolyhedron:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_outerpolyhedron, author="Wolfram Research", title="{OuterPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/OuterPolyhedron.html}", note=[Accessed: 21-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_outerpolyhedron, organization={Wolfram Research}, title={OuterPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/OuterPolyhedron.html}, note=[Accessed: 21-June-2024 ]}