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CanonicalizePolyhedron[poly]

给出多面体 poly 的标准表示，其中包含共享坐标和内外边界.

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范例  
基本范例  
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CanonicalizePolyhedron

CanonicalizePolyhedron[poly]

给出多面体 poly 的标准表示，其中包含共享坐标和内外边界.

更多信息

  • CanonicalizePolyhedron 用于从各种表示和描述中获取多面体的简单标准表示.
  • CanonicalizePolyhedron 将多面体转换为最优的标准形式 Polyhedron[{p1,p2,…},{outer1,outer2inner2,…}].
  • 点 pi 是非交叉多边形面的顶点，并按 Sort 顺序排序.
  • 外边界 outeri 是由多边形面 {fi1,fi2,…} 组成的闭合曲面，可能在边处相交.
  • 内边界 inneri 是由多边形面 {fj1,fj2,…} 组成的闭合曲面，可能在边处相交.

范例

打开所有单元 关闭所有单元

基本范例  (1)

给出 Polyhedron 的标准形式：

Wolfram Language code: 𝒫 = Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}];
Wolfram Language code: CanonicalizePolyhedron[𝒫]
Wolfram Language code: Graphics3D[%]

范围  (3)

CanonicalizePolyhedron 适用于多面体：

Wolfram Language code: Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}];
Wolfram Language code: CanonicalizePolyhedron[%]

Tetrahedron：

Wolfram Language code: CanonicalizePolyhedron[Tetrahedron[]]

Octahedron：

Wolfram Language code: CanonicalizePolyhedron[Octahedron[]]

有孔隙的多面体：

Wolfram Language code: 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: CanonicalizePolyhedron[%]
Wolfram Language code: Graphics3D[{Opacity[0.5], %}]

组件不相连的多面体：

Wolfram Language code: 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: CanonicalizePolyhedron[%]

应用  (1)

设置带有共享坐标的图形复合体:

Wolfram Language code: 𝒞𝒫 = CanonicalizePolyhedron[Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}]]
Wolfram Language code: Graphics3D[{GraphicsComplex[𝒞𝒫[[1]], Polyhedron[𝒞𝒫[[2]]]]}]

属性和关系  (5)

使用 CanonicalizePolyhedron 获取 PolyhedronCoordinates：

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]

柏拉图式实体的 CanonicalizePolyhedron 是一个多面体：

Wolfram Language code: CanonicalizePolyhedron[Icosahedron[]]

简单多面体的 CanonicalizePolyhedron 保留多面体坐标数：

Wolfram Language code: 𝒫 = Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}];
Wolfram Language code: SimplePolyhedronQ[𝒫]
Wolfram Language code: Length[PolyhedronCoordinates[#]]& /@ {𝒫, CanonicalizePolyhedron[𝒫]}

OuterPolyhedron 给出外多面体的标准表示：

Wolfram Language code: OuterPolyhedron[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}}]]

InnerPolyhedron 给出内多面体的标准表示：

Wolfram Language code: InnerPolyhedron[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}}]]

可能存在的问题  (1)

CanonicalizePoyhedron 只适用于几何区域：

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}}, {{2, 3, 4}, {3, 2, 1}}];
Wolfram Language code: {CanonicalizePolyhedron[𝒫], RegionQ[𝒫]}
Wolfram Research (2019)，CanonicalizePolyhedron，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html.

文本

Wolfram Research (2019)，CanonicalizePolyhedron，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html.

CMS

Wolfram 语言. 2019. "CanonicalizePolyhedron." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html.

APA

Wolfram 语言. (2019). CanonicalizePolyhedron. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html 年

BibTeX

@misc{reference.wolfram_2026_canonicalizepolyhedron, author="Wolfram Research", title="{CanonicalizePolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html}", note=[Accessed: 10-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_canonicalizepolyhedron, organization={Wolfram Research}, title={CanonicalizePolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html}, note=[Accessed: 10-September-2026]}