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PolyhedronCoordinates[poly]

gives a list of coordinates in the polyhedron poly.

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Basic Examples  
Scope  
Properties & Relations  
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PolyhedronCoordinates

PolyhedronCoordinates[poly]

gives a list of coordinates in the polyhedron poly.

Details

  • PolyhedronCoordinates is also known as polyhedron vertex coordinates.
  • PolyhedronCoordinates is defined by the canonicalization performed in CanonicalizePolyhedron.
  • PolyhedronCoordinates gives a list of coordinates {p1,p2,…}.
  • For a polyhedron with self-intersections, the resulting coordinate list will also include intersection points.
  • For a polyhedron defined with repeated coordinates, the resulting coordinate list removes duplicate coordinates.

Examples

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Basic Examples  (1)

Get the vertex coordinates from a Polyhedron:

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 0, 1}, {0, 1, 1}, {1, 1, 1}, {1, 0, 1}}, {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}}];
Wolfram Language code: PolyhedronCoordinates[𝒫]

Scope  (3)

PolyhedronCoordinates works on polyhedrons:

Wolfram Language code: Polyhedron[{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 0, 1}, {0, 1, 1}, {1, 1, 1}, {1, 0, 1}}, {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}}];
Wolfram Language code: PolyhedronCoordinates[%]

Tetrahedron:

Wolfram Language code: PolyhedronCoordinates[Tetrahedron[]]
Wolfram Language code: Graphics3D[Tetrahedron[]]

Cube:

Wolfram Language code: PolyhedronCoordinates[Cube[]]

Polyhedron with holes:

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {0, 3, 0}, {3, 3, 0}, {3, 0, 0}, {0, 0, 3}, {0, 3, 3}, {3, 3, 3}, {3, 0, 3}, {1, 1, 1}, {1, 2, 1}, {2, 2, 1}, {2, 1, 1}, {1, 1, 2}, {1, 2, 2}, {2, 2, 2}, {2, 1, 2}}, {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}} -> {{{10, 11, 12, 9}, {9, 12, 16, 13}, {12, 11, 15, 16}, {11, 10, 14, 15}, {10, 9, 13, 14}, {13, 16, 15, 14}}}];
Wolfram Language code: PolyhedronCoordinates[𝒫]
Wolfram Language code: Region[Style[𝒫, Opacity[.5]]]

Polyhedrons with disconnected components:

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 1, 1}, {2, 1, 1}, {1, 2, 1}, {1, 1, 2}}, {{{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}}, {{5, 6, 7}, {5, 6, 8}, {6, 7, 8}, {5, 7, 8}}}]
Wolfram Language code: PolyhedronCoordinates[𝒫]

Properties & Relations  (2)

Using CanonicalizePolyhedron to get polyhedron coordinates:

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 0, 1}, {0, 1, 1}, {1, 1, 1}, {1, 0, 1}}, {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}}];
Wolfram Language code: First[CanonicalizePolyhedron[𝒫]]
Wolfram Language code: PolyhedronCoordinates[𝒫]

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

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}}];
Wolfram Language code: SimplePolyhedronQ[𝒫]
Wolfram Language code: PolyhedronCoordinates[𝒫]
Wolfram Language code: PolyhedronCoordinates[OuterPolyhedron[𝒫]]
Wolfram Research (2019), PolyhedronCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/PolyhedronCoordinates.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_polyhedroncoordinates, author="Wolfram Research", title="{PolyhedronCoordinates}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolyhedronCoordinates.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_polyhedroncoordinates, organization={Wolfram Research}, title={PolyhedronCoordinates}, year={2019}, url={https://reference.wolfram.com/language/ref/PolyhedronCoordinates.html}, note=[Accessed: 13-June-2026]}