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PolyhedronDecomposition[poly]

decomposes the polyhedron poly into a union of simpler polyhedra.

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PolyhedronDecomposition

PolyhedronDecomposition[poly]

decomposes the polyhedron poly into a union of simpler polyhedra.

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Examples

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Basic Examples  (1)

Decompose a Polyhedron into a union of simpler polyhedra:

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: PolyhedronDecomposition[𝒫]//Shallow
Wolfram Language code: Graphics3D[{%}]

Scope  (2)

Decompose polyhedra with voids:

Wolfram Language code: 𝒫 = Polyhedron[{{-Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0]}, {Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (-3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0]}, {R ... }, {11, 12, 8, 16, 7}, {12, 6, 20, 4, 8}, {6, 2, 13, 18, 20}, {2, 5, 19, 17, 13}, {4, 20, 18, 10, 15}, {18, 13, 17, 9, 10}, {17, 19, 3, 14, 9}, {3, 7, 16, 1, 14}, {16, 8, 4, 15, 1}, {22, 23, 24}, {23, 22, 21}, {24, 21, 22}, {21, 24, 23}}];
Wolfram Language code: PolyhedronDecomposition[𝒫]//Shallow
Wolfram Language code: Graphics3D[{Opacity[.5], %}]

Disconnected components:

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, 2, 2}, {2, 3, 2}, {3, 3, 2}, {3, 2, 2}, {2, 2, 3}, {2, 3, 3}, {3, 3, 3}, {3, 2, 3}}, {{{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: PolyhedronDecomposition[𝒫]//Shallow
Wolfram Language code: Graphics3D[%]
Wolfram Research (2019), PolyhedronDecomposition, Wolfram Language function, https://reference.wolfram.com/language/ref/PolyhedronDecomposition.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_polyhedrondecomposition, author="Wolfram Research", title="{PolyhedronDecomposition}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolyhedronDecomposition.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_polyhedrondecomposition, organization={Wolfram Research}, title={PolyhedronDecomposition}, year={2019}, url={https://reference.wolfram.com/language/ref/PolyhedronDecomposition.html}, note=[Accessed: 12-June-2026]}